Best Known (62−30, 62, s)-Nets in Base 256
(62−30, 62, 4369)-Net over F256 — Constructive and digital
Digital (32, 62, 4369)-net over F256, using
- 2561 times duplication [i] based on digital (31, 61, 4369)-net over F256, using
- t-expansion [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
- t-expansion [i] based on digital (30, 61, 4369)-net over F256, using
(62−30, 62, 15413)-Net over F256 — Digital
Digital (32, 62, 15413)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25662, 15413, F256, 4, 30) (dual of [(15413, 4), 61590, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25662, 16386, F256, 4, 30) (dual of [(16386, 4), 65482, 31]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25661, 16386, F256, 4, 30) (dual of [(16386, 4), 65483, 31]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25661, 65544, F256, 30) (dual of [65544, 65483, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [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(25653, 65536, F256, 27) (dual of [65536, 65483, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- OOA 4-folding [i] based on linear OA(25661, 65544, F256, 30) (dual of [65544, 65483, 31]-code), using
- 2561 times duplication [i] based on linear OOA(25661, 16386, F256, 4, 30) (dual of [(16386, 4), 65483, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25662, 16386, F256, 4, 30) (dual of [(16386, 4), 65482, 31]-NRT-code), using
(62−30, 62, large)-Net in Base 256 — Upper bound on s
There is no (32, 62, large)-net in base 256, because
- 28 times m-reduction [i] would yield (32, 34, large)-net in base 256, but