Best Known (92, 114, s)-Nets in Base 16
(92, 114, 95358)-Net over F16 — Constructive and digital
Digital (92, 114, 95358)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 13, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-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 (2, 13, 33)-net over F16, using
(92, 114, 190650)-Net in Base 16 — Constructive
(92, 114, 190650)-net in base 16, using
- 162 times duplication [i] based on (90, 112, 190650)-net in base 16, using
- base change [i] based on digital (42, 64, 190650)-net over F128, using
- net defined by OOA [i] based on linear OOA(12864, 190650, F128, 22, 22) (dual of [(190650, 22), 4194236, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12864, 2097150, F128, 22) (dual of [2097150, 2097086, 23]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(12864, 2097150, F128, 22) (dual of [2097150, 2097086, 23]-code), using
- net defined by OOA [i] based on linear OOA(12864, 190650, F128, 22, 22) (dual of [(190650, 22), 4194236, 23]-NRT-code), using
- base change [i] based on digital (42, 64, 190650)-net over F128, using
(92, 114, 1990925)-Net over F16 — Digital
Digital (92, 114, 1990925)-net over F16, using
(92, 114, large)-Net in Base 16 — Upper bound on s
There is no (92, 114, large)-net in base 16, because
- 20 times m-reduction [i] would yield (92, 94, large)-net in base 16, but