Best Known (74, 74+26, s)-Nets in Base 16
(74, 74+26, 5042)-Net over F16 — Constructive and digital
Digital (74, 100, 5042)-net over F16, using
- 161 times duplication [i] based on digital (73, 99, 5042)-net over F16, using
- net defined by OOA [i] based on linear OOA(1699, 5042, F16, 26, 26) (dual of [(5042, 26), 130993, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(1699, 65546, F16, 26) (dual of [65546, 65447, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(1699, 65550, F16, 26) (dual of [65550, 65451, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(1697, 65536, F16, 26) (dual of [65536, 65439, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(1685, 65536, F16, 23) (dual of [65536, 65451, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(1699, 65550, F16, 26) (dual of [65550, 65451, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(1699, 65546, F16, 26) (dual of [65546, 65447, 27]-code), using
- net defined by OOA [i] based on linear OOA(1699, 5042, F16, 26, 26) (dual of [(5042, 26), 130993, 27]-NRT-code), using
(74, 74+26, 60559)-Net over F16 — Digital
Digital (74, 100, 60559)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16100, 60559, F16, 26) (dual of [60559, 60459, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16100, 65554, F16, 26) (dual of [65554, 65454, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(1697, 65536, F16, 26) (dual of [65536, 65439, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(1681, 65536, F16, 22) (dual of [65536, 65455, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(16100, 65554, F16, 26) (dual of [65554, 65454, 27]-code), using
(74, 74+26, large)-Net in Base 16 — Upper bound on s
There is no (74, 100, large)-net in base 16, because
- 24 times m-reduction [i] would yield (74, 76, large)-net in base 16, but