Best Known (130−29, 130, s)-Nets in Base 16
(130−29, 130, 9395)-Net over F16 — Constructive and digital
Digital (101, 130, 9395)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 16, 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 (85, 114, 9362)-net over F16, using
- net defined by OOA [i] based on linear OOA(16114, 9362, F16, 29, 29) (dual of [(9362, 29), 271384, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(16114, 131069, F16, 29) (dual of [131069, 130955, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(16114, 131074, F16, 29) (dual of [131074, 130960, 30]-code), using
- trace code [i] based on linear OA(25657, 65537, F256, 29) (dual of [65537, 65480, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- trace code [i] based on linear OA(25657, 65537, F256, 29) (dual of [65537, 65480, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(16114, 131074, F16, 29) (dual of [131074, 130960, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(16114, 131069, F16, 29) (dual of [131069, 130955, 30]-code), using
- net defined by OOA [i] based on linear OOA(16114, 9362, F16, 29, 29) (dual of [(9362, 29), 271384, 30]-NRT-code), using
- digital (2, 16, 33)-net over F16, using
(130−29, 130, 18725)-Net in Base 16 — Constructive
(101, 130, 18725)-net in base 16, using
- 161 times duplication [i] based on (100, 129, 18725)-net in base 16, using
- base change [i] based on digital (57, 86, 18725)-net over F64, using
- net defined by OOA [i] based on linear OOA(6486, 18725, F64, 29, 29) (dual of [(18725, 29), 542939, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(6486, 262151, F64, 29) (dual of [262151, 262065, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(6486, 262152, F64, 29) (dual of [262152, 262066, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- linear OA(6485, 262145, F64, 29) (dual of [262145, 262060, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(6479, 262145, F64, 27) (dual of [262145, 262066, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6486, 262152, F64, 29) (dual of [262152, 262066, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(6486, 262151, F64, 29) (dual of [262151, 262065, 30]-code), using
- net defined by OOA [i] based on linear OOA(6486, 18725, F64, 29, 29) (dual of [(18725, 29), 542939, 30]-NRT-code), using
- base change [i] based on digital (57, 86, 18725)-net over F64, using
(130−29, 130, 293421)-Net over F16 — Digital
Digital (101, 130, 293421)-net over F16, using
(130−29, 130, large)-Net in Base 16 — Upper bound on s
There is no (101, 130, large)-net in base 16, because
- 27 times m-reduction [i] would yield (101, 103, large)-net in base 16, but