Best Known (29−10, 29, s)-Nets in Base 256
(29−10, 29, 1677720)-Net over F256 — Constructive and digital
Digital (19, 29, 1677720)-net over F256, using
- 2561 times duplication [i] based on digital (18, 28, 1677720)-net over F256, using
- net defined by OOA [i] based on linear OOA(25628, 1677720, F256, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(25628, 8388600, F256, 10) (dual of [8388600, 8388572, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(25628, 8388600, F256, 10) (dual of [8388600, 8388572, 11]-code), using
- net defined by OOA [i] based on linear OOA(25628, 1677720, F256, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
(29−10, 29, 4194301)-Net over F256 — Digital
Digital (19, 29, 4194301)-net over F256, using
- 2561 times duplication [i] based on digital (18, 28, 4194301)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25628, 4194301, F256, 2, 10) (dual of [(4194301, 2), 8388574, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25628, 8388602, F256, 10) (dual of [8388602, 8388574, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- OOA 2-folding [i] based on linear OA(25628, 8388602, F256, 10) (dual of [8388602, 8388574, 11]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25628, 4194301, F256, 2, 10) (dual of [(4194301, 2), 8388574, 11]-NRT-code), using
(29−10, 29, large)-Net in Base 256 — Upper bound on s
There is no (19, 29, large)-net in base 256, because
- 8 times m-reduction [i] would yield (19, 21, large)-net in base 256, but