Best Known (56, 56+35, s)-Nets in Base 64
(56, 56+35, 690)-Net over F64 — Constructive and digital
Digital (56, 91, 690)-net over F64, using
- 641 times duplication [i] based on digital (55, 90, 690)-net over F64, using
- t-expansion [i] based on digital (53, 90, 690)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (28, 65, 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 (7, 25, 177)-net over F64, using
- (u, u+v)-construction [i] based on
- t-expansion [i] based on digital (53, 90, 690)-net over F64, using
(56, 56+35, 965)-Net in Base 64 — Constructive
(56, 91, 965)-net in base 64, using
- base change [i] based on digital (43, 78, 965)-net over F128, using
- 1282 times duplication [i] based on digital (41, 76, 965)-net over F128, using
- net defined by OOA [i] based on linear OOA(12876, 965, F128, 35, 35) (dual of [(965, 35), 33699, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(12876, 16406, F128, 35) (dual of [16406, 16330, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(12876, 16408, F128, 35) (dual of [16408, 16332, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- linear OA(12869, 16385, F128, 35) (dual of [16385, 16316, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(12853, 16385, F128, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(1287, 23, F128, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12876, 16408, F128, 35) (dual of [16408, 16332, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(12876, 16406, F128, 35) (dual of [16406, 16330, 36]-code), using
- net defined by OOA [i] based on linear OOA(12876, 965, F128, 35, 35) (dual of [(965, 35), 33699, 36]-NRT-code), using
- 1282 times duplication [i] based on digital (41, 76, 965)-net over F128, using
(56, 56+35, 14683)-Net over F64 — Digital
Digital (56, 91, 14683)-net over F64, using
(56, 56+35, large)-Net in Base 64 — Upper bound on s
There is no (56, 91, large)-net in base 64, because
- 33 times m-reduction [i] would yield (56, 58, large)-net in base 64, but