Best Known (96, 96+23, s)-Nets in Base 16
(96, 96+23, 95358)-Net over F16 — Constructive and digital
Digital (96, 119, 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 (83, 106, 95325)-net over F16, using
- net defined by OOA [i] based on linear OOA(16106, 95325, F16, 23, 23) (dual of [(95325, 23), 2192369, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using
- net defined by OOA [i] based on linear OOA(16106, 95325, F16, 23, 23) (dual of [(95325, 23), 2192369, 24]-NRT-code), using
- digital (2, 13, 33)-net over F16, using
(96, 96+23, 190650)-Net in Base 16 — Constructive
(96, 119, 190650)-net in base 16, using
- base change [i] based on digital (45, 68, 190650)-net over F128, using
- 1281 times duplication [i] based on digital (44, 67, 190650)-net over F128, using
- net defined by OOA [i] based on linear OOA(12867, 190650, F128, 23, 23) (dual of [(190650, 23), 4384883, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12867, 2097151, F128, 23) (dual of [2097151, 2097084, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(12867, 2097152, F128, 23) (dual of [2097152, 2097085, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(12867, 2097152, F128, 23) (dual of [2097152, 2097085, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12867, 2097151, F128, 23) (dual of [2097151, 2097084, 24]-code), using
- net defined by OOA [i] based on linear OOA(12867, 190650, F128, 23, 23) (dual of [(190650, 23), 4384883, 24]-NRT-code), using
- 1281 times duplication [i] based on digital (44, 67, 190650)-net over F128, using
(96, 96+23, 1967699)-Net over F16 — Digital
Digital (96, 119, 1967699)-net over F16, using
(96, 96+23, large)-Net in Base 16 — Upper bound on s
There is no (96, 119, large)-net in base 16, because
- 21 times m-reduction [i] would yield (96, 98, large)-net in base 16, but