Best Known (16, 16+13, s)-Nets in Base 256
(16, 16+13, 10924)-Net over F256 — Constructive and digital
Digital (16, 29, 10924)-net over F256, using
- 2561 times duplication [i] based on digital (15, 28, 10924)-net over F256, using
- net defined by OOA [i] based on linear OOA(25628, 10924, F256, 13, 13) (dual of [(10924, 13), 141984, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25628, 65545, F256, 13) (dual of [65545, 65517, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25628, 65548, F256, 13) (dual of [65548, 65520, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25628, 65548, F256, 13) (dual of [65548, 65520, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25628, 65545, F256, 13) (dual of [65545, 65517, 14]-code), using
- net defined by OOA [i] based on linear OOA(25628, 10924, F256, 13, 13) (dual of [(10924, 13), 141984, 14]-NRT-code), using
(16, 16+13, 32775)-Net over F256 — Digital
Digital (16, 29, 32775)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25629, 32775, F256, 2, 13) (dual of [(32775, 2), 65521, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25629, 65550, F256, 13) (dual of [65550, 65521, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- OOA 2-folding [i] based on linear OA(25629, 65550, F256, 13) (dual of [65550, 65521, 14]-code), using
(16, 16+13, large)-Net in Base 256 — Upper bound on s
There is no (16, 29, large)-net in base 256, because
- 11 times m-reduction [i] would yield (16, 18, large)-net in base 256, but