Best Known (85, 107, s)-Nets in Base 16
(85, 107, 95327)-Net over F16 — Constructive and digital
Digital (85, 107, 95327)-net over F16, using
- 162 times duplication [i] based on digital (83, 105, 95327)-net over F16, using
- net defined by OOA [i] based on linear OOA(16105, 95327, F16, 22, 22) (dual of [(95327, 22), 2097089, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(16105, 1048597, F16, 22) (dual of [1048597, 1048492, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(16105, 1048600, F16, 22) (dual of [1048600, 1048495, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(164, 24, F16, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,16)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(16105, 1048600, F16, 22) (dual of [1048600, 1048495, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(16105, 1048597, F16, 22) (dual of [1048597, 1048492, 23]-code), using
- net defined by OOA [i] based on linear OOA(16105, 95327, F16, 22, 22) (dual of [(95327, 22), 2097089, 23]-NRT-code), using
(85, 107, 1048607)-Net over F16 — Digital
Digital (85, 107, 1048607)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16107, 1048607, F16, 22) (dual of [1048607, 1048500, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(166, 31, F16, 4) (dual of [31, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(166, 240, F16, 4) (dual of [240, 234, 5]-code), using
- 1 times truncation [i] based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(166, 240, F16, 4) (dual of [240, 234, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
(85, 107, large)-Net in Base 16 — Upper bound on s
There is no (85, 107, large)-net in base 16, because
- 20 times m-reduction [i] would yield (85, 87, large)-net in base 16, but