Best Known (37−21, 37, s)-Nets in Base 256
(37−21, 37, 520)-Net over F256 — Constructive and digital
Digital (16, 37, 520)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (3, 24, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256 (see above)
- digital (3, 13, 260)-net over F256, using
(37−21, 37, 1128)-Net over F256 — Digital
Digital (16, 37, 1128)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25637, 1128, F256, 21) (dual of [1128, 1091, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25637, 1285, F256, 21) (dual of [1285, 1248, 22]-code), using
(37−21, 37, 8300414)-Net in Base 256 — Upper bound on s
There is no (16, 37, 8300415)-net in base 256, because
- 1 times m-reduction [i] would yield (16, 36, 8300415)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 497 323764 105920 267266 020415 894155 148182 510494 797524 311294 719492 001347 009021 784928 668251 > 25636 [i]