Best Known (94, 94+22, s)-Nets in Base 16
(94, 94+22, 95370)-Net over F16 — Constructive and digital
Digital (94, 116, 95370)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (4, 15, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- digital (79, 101, 95325)-net over F16, using
- net defined by OOA [i] based on linear OOA(16101, 95325, F16, 22, 22) (dual of [(95325, 22), 2097049, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(16101, 1048575, F16, 22) (dual of [1048575, 1048474, 23]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(16101, 1048575, F16, 22) (dual of [1048575, 1048474, 23]-code), using
- net defined by OOA [i] based on linear OOA(16101, 95325, F16, 22, 22) (dual of [(95325, 22), 2097049, 23]-NRT-code), using
- digital (4, 15, 45)-net over F16, using
(94, 94+22, 190651)-Net in Base 16 — Constructive
(94, 116, 190651)-net in base 16, using
- net defined by OOA [i] based on OOA(16116, 190651, S16, 22, 22), using
- OA 11-folding and stacking [i] based on OA(16116, 2097161, S16, 22), using
- discarding factors based on OA(16116, 2097163, S16, 22), using
- discarding parts of the base [i] based on linear OA(12866, 2097163, F128, 22) (dual of [2097163, 2097097, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12855, 2097152, F128, 19) (dual of [2097152, 2097097, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding parts of the base [i] based on linear OA(12866, 2097163, F128, 22) (dual of [2097163, 2097097, 23]-code), using
- discarding factors based on OA(16116, 2097163, S16, 22), using
- OA 11-folding and stacking [i] based on OA(16116, 2097161, S16, 22), using
(94, 94+22, 2592582)-Net over F16 — Digital
Digital (94, 116, 2592582)-net over F16, using
(94, 94+22, large)-Net in Base 16 — Upper bound on s
There is no (94, 116, large)-net in base 16, because
- 20 times m-reduction [i] would yield (94, 96, large)-net in base 16, but