Best Known (33, 66, s)-Nets in Base 256
(33, 66, 4096)-Net over F256 — Constructive and digital
Digital (33, 66, 4096)-net over F256, using
- 2561 times duplication [i] based on digital (32, 65, 4096)-net over F256, using
- net defined by OOA [i] based on linear OOA(25665, 4096, F256, 33, 33) (dual of [(4096, 33), 135103, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- OOA 16-folding and stacking with additional row [i] based on linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using
- net defined by OOA [i] based on linear OOA(25665, 4096, F256, 33, 33) (dual of [(4096, 33), 135103, 34]-NRT-code), using
(33, 66, 11810)-Net over F256 — Digital
Digital (33, 66, 11810)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25666, 11810, F256, 5, 33) (dual of [(11810, 5), 58984, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25666, 13108, F256, 5, 33) (dual of [(13108, 5), 65474, 34]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25666, 65540, F256, 33) (dual of [65540, 65474, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(25666, 65542, F256, 33) (dual of [65542, 65476, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,15]) [i] based on
- linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(25661, 65537, F256, 31) (dual of [65537, 65476, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 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([0,16]) ⊂ C([0,15]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25666, 65542, F256, 33) (dual of [65542, 65476, 34]-code), using
- OOA 5-folding [i] based on linear OA(25666, 65540, F256, 33) (dual of [65540, 65474, 34]-code), using
- discarding factors / shortening the dual code based on linear OOA(25666, 13108, F256, 5, 33) (dual of [(13108, 5), 65474, 34]-NRT-code), using
(33, 66, large)-Net in Base 256 — Upper bound on s
There is no (33, 66, large)-net in base 256, because
- 31 times m-reduction [i] would yield (33, 35, large)-net in base 256, but