Best Known (30, 30+30, s)-Nets in Base 256
(30, 30+30, 4369)-Net over F256 — Constructive and digital
Digital (30, 60, 4369)-net over F256, using
- 1 times m-reduction [i] based on digital (30, 61, 4369)-net over F256, using
- net defined by OOA [i] based on linear OOA(25661, 4369, F256, 31, 31) (dual of [(4369, 31), 135378, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(25661, 65536, F256, 31) (dual of [65536, 65475, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- OOA 15-folding and stacking with additional row [i] based on linear OA(25661, 65536, F256, 31) (dual of [65536, 65475, 32]-code), using
- net defined by OOA [i] based on linear OOA(25661, 4369, F256, 31, 31) (dual of [(4369, 31), 135378, 32]-NRT-code), using
(30, 30+30, 12686)-Net over F256 — Digital
Digital (30, 60, 12686)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25660, 12686, F256, 5, 30) (dual of [(12686, 5), 63370, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25660, 13108, F256, 5, 30) (dual of [(13108, 5), 65480, 31]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25660, 65540, F256, 30) (dual of [65540, 65480, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(25660, 65541, F256, 30) (dual of [65541, 65481, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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 Ce(29) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(25660, 65541, F256, 30) (dual of [65541, 65481, 31]-code), using
- OOA 5-folding [i] based on linear OA(25660, 65540, F256, 30) (dual of [65540, 65480, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(25660, 13108, F256, 5, 30) (dual of [(13108, 5), 65480, 31]-NRT-code), using
(30, 30+30, large)-Net in Base 256 — Upper bound on s
There is no (30, 60, large)-net in base 256, because
- 28 times m-reduction [i] would yield (30, 32, large)-net in base 256, but