Best Known (20, 20+21, s)-Nets in Base 256
(20, 20+21, 6553)-Net over F256 — Constructive and digital
Digital (20, 41, 6553)-net over F256, using
- net defined by OOA [i] based on linear OOA(25641, 6553, F256, 21, 21) (dual of [(6553, 21), 137572, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25641, 65531, F256, 21) (dual of [65531, 65490, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25641, 65531, F256, 21) (dual of [65531, 65490, 22]-code), using
(20, 20+21, 13107)-Net over F256 — Digital
Digital (20, 41, 13107)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25641, 13107, F256, 5, 21) (dual of [(13107, 5), 65494, 22]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25641, 65535, F256, 21) (dual of [65535, 65494, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using
- OOA 5-folding [i] based on linear OA(25641, 65535, F256, 21) (dual of [65535, 65494, 22]-code), using
(20, 20+21, large)-Net in Base 256 — Upper bound on s
There is no (20, 41, large)-net in base 256, because
- 19 times m-reduction [i] would yield (20, 22, large)-net in base 256, but