Best Known (21, 21+31, s)-Nets in Base 256
(21, 21+31, 520)-Net over F256 — Constructive and digital
Digital (21, 52, 520)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (3, 34, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256 (see above)
- digital (3, 18, 260)-net over F256, using
(21, 21+31, 774)-Net over F256 — Digital
Digital (21, 52, 774)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25652, 774, F256, 31) (dual of [774, 722, 32]-code), using
- construction X applied to C([242,272]) ⊂ C([244,272]) [i] based on
- linear OA(25651, 771, F256, 31) (dual of [771, 720, 32]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {242,243,…,272}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(25649, 771, F256, 29) (dual of [771, 722, 30]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {244,245,…,272}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([242,272]) ⊂ C([244,272]) [i] based on
(21, 21+31, 3883663)-Net in Base 256 — Upper bound on s
There is no (21, 52, 3883664)-net in base 256, because
- 1 times m-reduction [i] would yield (21, 51, 3883664)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 661 058168 143441 441559 339040 136405 632113 499792 273262 720133 748526 938139 259795 301337 313504 155395 982891 570821 352735 321839 893551 > 25651 [i]