Best Known (45−23, 45, s)-Nets in Base 256
(45−23, 45, 5957)-Net over F256 — Constructive and digital
Digital (22, 45, 5957)-net over F256, using
- net defined by OOA [i] based on linear OOA(25645, 5957, F256, 23, 23) (dual of [(5957, 23), 136966, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25645, 65528, F256, 23) (dual of [65528, 65483, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25645, 65528, F256, 23) (dual of [65528, 65483, 24]-code), using
(45−23, 45, 13050)-Net over F256 — Digital
Digital (22, 45, 13050)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25645, 13050, F256, 5, 23) (dual of [(13050, 5), 65205, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25645, 13107, F256, 5, 23) (dual of [(13107, 5), 65490, 24]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25645, 65535, F256, 23) (dual of [65535, 65490, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using
- OOA 5-folding [i] based on linear OA(25645, 65535, F256, 23) (dual of [65535, 65490, 24]-code), using
- discarding factors / shortening the dual code based on linear OOA(25645, 13107, F256, 5, 23) (dual of [(13107, 5), 65490, 24]-NRT-code), using
(45−23, 45, large)-Net in Base 256 — Upper bound on s
There is no (22, 45, large)-net in base 256, because
- 21 times m-reduction [i] would yield (22, 24, large)-net in base 256, but