Best Known (37−19, 37, s)-Nets in Base 256
(37−19, 37, 7281)-Net over F256 — Constructive and digital
Digital (18, 37, 7281)-net over F256, using
- net defined by OOA [i] based on linear OOA(25637, 7281, F256, 19, 19) (dual of [(7281, 19), 138302, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25637, 65530, F256, 19) (dual of [65530, 65493, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25637, 65530, F256, 19) (dual of [65530, 65493, 20]-code), using
(37−19, 37, 13107)-Net over F256 — Digital
Digital (18, 37, 13107)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25637, 13107, F256, 5, 19) (dual of [(13107, 5), 65498, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25637, 65535, F256, 19) (dual of [65535, 65498, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using
- OOA 5-folding [i] based on linear OA(25637, 65535, F256, 19) (dual of [65535, 65498, 20]-code), using
(37−19, 37, large)-Net in Base 256 — Upper bound on s
There is no (18, 37, large)-net in base 256, because
- 17 times m-reduction [i] would yield (18, 20, large)-net in base 256, but