Best Known (75−29, 75, s)-Nets in Base 64
(75−29, 75, 617)-Net over F64 — Constructive and digital
Digital (46, 75, 617)-net over F64, using
- 1 times m-reduction [i] based on digital (46, 76, 617)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- digital (28, 58, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- digital (3, 18, 104)-net over F64, using
- (u, u+v)-construction [i] based on
(75−29, 75, 1171)-Net in Base 64 — Constructive
(46, 75, 1171)-net in base 64, using
- 645 times duplication [i] based on (41, 70, 1171)-net in base 64, using
- base change [i] based on digital (31, 60, 1171)-net over F128, using
- net defined by OOA [i] based on linear OOA(12860, 1171, F128, 29, 29) (dual of [(1171, 29), 33899, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12860, 16395, F128, 29) (dual of [16395, 16335, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(12860, 16396, F128, 29) (dual of [16396, 16336, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(12857, 16385, F128, 29) (dual of [16385, 16328, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(12849, 16385, F128, 25) (dual of [16385, 16336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12860, 16396, F128, 29) (dual of [16396, 16336, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12860, 16395, F128, 29) (dual of [16395, 16335, 30]-code), using
- net defined by OOA [i] based on linear OOA(12860, 1171, F128, 29, 29) (dual of [(1171, 29), 33899, 30]-NRT-code), using
- base change [i] based on digital (31, 60, 1171)-net over F128, using
(75−29, 75, 12363)-Net over F64 — Digital
Digital (46, 75, 12363)-net over F64, using
(75−29, 75, large)-Net in Base 64 — Upper bound on s
There is no (46, 75, large)-net in base 64, because
- 27 times m-reduction [i] would yield (46, 48, large)-net in base 64, but