Best Known (72, 91, s)-Nets in Base 16
(72, 91, 116511)-Net over F16 — Constructive and digital
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
(72, 91, 1048601)-Net over F16 — Digital
Digital (72, 91, 1048601)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1691, 1048601, F16, 19) (dual of [1048601, 1048510, 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, 25, F16, 4) (dual of [25, 20, 5]-code), using
- extended algebraic-geometric code AGe(F,20P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 25, using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
(72, 91, large)-Net in Base 16 — Upper bound on s
There is no (72, 91, large)-net in base 16, because
- 17 times m-reduction [i] would yield (72, 74, large)-net in base 16, but