Best Known (74, 74+19, s)-Nets in Base 16
(74, 74+19, 116511)-Net over F16 — Constructive and digital
Digital (74, 93, 116511)-net over F16, using
- 162 times duplication [i] based on digital (72, 91, 116511)-net over F16, using
- net defined by OOA [i] based on linear OOA(1691, 116511, F16, 19, 19) (dual of [(116511, 19), 2213618, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(1691, 1048600, F16, 19) (dual of [1048600, 1048509, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1666, 1048576, F16, 14) (dual of [1048576, 1048510, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(165, 24, F16, 4) (dual of [24, 19, 5]-code), using
- extended algebraic-geometric code AGe(F,19P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- OOA 9-folding and stacking with additional row [i] based on linear OA(1691, 1048600, F16, 19) (dual of [1048600, 1048509, 20]-code), using
- net defined by OOA [i] based on linear OOA(1691, 116511, F16, 19, 19) (dual of [(116511, 19), 2213618, 20]-NRT-code), using
(74, 74+19, 1048608)-Net over F16 — Digital
Digital (74, 93, 1048608)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1693, 1048608, F16, 19) (dual of [1048608, 1048515, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1661, 1048576, F16, 13) (dual of [1048576, 1048515, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(167, 32, F16, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
(74, 74+19, large)-Net in Base 16 — Upper bound on s
There is no (74, 93, large)-net in base 16, because
- 17 times m-reduction [i] would yield (74, 76, large)-net in base 16, but