Best Known (102−23, 102, s)-Nets in Base 16
(102−23, 102, 11939)-Net over F16 — Constructive and digital
Digital (79, 102, 11939)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- digital (67, 90, 11915)-net over F16, using
- net defined by OOA [i] based on linear OOA(1690, 11915, F16, 23, 23) (dual of [(11915, 23), 273955, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(1690, 131066, F16, 23) (dual of [131066, 130976, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(1690, 131074, F16, 23) (dual of [131074, 130984, 24]-code), using
- trace code [i] based on linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- trace code [i] based on linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(1690, 131074, F16, 23) (dual of [131074, 130984, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(1690, 131066, F16, 23) (dual of [131066, 130976, 24]-code), using
- net defined by OOA [i] based on linear OOA(1690, 11915, F16, 23, 23) (dual of [(11915, 23), 273955, 24]-NRT-code), using
- digital (1, 12, 24)-net over F16, using
(102−23, 102, 23831)-Net in Base 16 — Constructive
(79, 102, 23831)-net in base 16, using
- base change [i] based on digital (45, 68, 23831)-net over F64, using
- 641 times duplication [i] based on digital (44, 67, 23831)-net over F64, using
- net defined by OOA [i] based on linear OOA(6467, 23831, F64, 23, 23) (dual of [(23831, 23), 548046, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6467, 262142, F64, 23) (dual of [262142, 262075, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6467, 262142, F64, 23) (dual of [262142, 262075, 24]-code), using
- net defined by OOA [i] based on linear OOA(6467, 23831, F64, 23, 23) (dual of [(23831, 23), 548046, 24]-NRT-code), using
- 641 times duplication [i] based on digital (44, 67, 23831)-net over F64, using
(102−23, 102, 230951)-Net over F16 — Digital
Digital (79, 102, 230951)-net over F16, using
(102−23, 102, large)-Net in Base 16 — Upper bound on s
There is no (79, 102, large)-net in base 16, because
- 21 times m-reduction [i] would yield (79, 81, large)-net in base 16, but