The 40 cap in AG(4,4).
For more information see The largest cap in AG(4,4) and its uniqueness.
1000120212121203012302200132121213021100
0100103301231133001101230123113300330123
0010011122223333000022222222333311112222
0000000000000000111111112222222233333333
1111111111111111111111111111111111111111
The prime polynomial used to generate GF(4) is: X2+X+1. The element f=aX+b, a,b in {0,1}, is written as the number a*2+b.
The weight distribution:
A'0= 1,
A'24= 15,
A'28= 360,
A'30= 480,
A'32= 45,
A'36= 120,
A'40= 3.
A0= 1,
A4= 8850,
A5= 155520,
A6= 2715720,
A7= 39830400,
A8= 493030665,
A9= 5254640640,
A10= 48883854144,
A11= 399921177600,
A12= 2899518786360,
A13= 18735163077120,
A14= 108396507811680,
A15= 563661954986496,
A16= 2642164808406210,
A17= 11190345416616960,
A18= 42896325426048960,
A19= 149008283301288960,
A20= 469376107672743180,
A21= 1341074553869794560,
A22= 3474602324145837360,
A23= 8157761902302946560,
A24= 17335244066991616410,
A25= 33283668663994199040,
A26= 57606349534835417280,
A27= 89609877026460564480,
A28= 124813757508016233720,
A29= 154941215821597094400,
A30= 170435337864502445664,
A31= 164937423331478376960,
A32= 139165951226845581405,
A33= 101211600722039239680,
A34= 62513047586763063360,
A35= 32149567298243478528,
A36= 13395653050888599090,
A37= 4344536122264567680,
A38= 1028969081983559880,
A39= 158302935647802240,
A40= 11872720175705661.