Best Known (48, 48+34, s)-Nets in Base 64
(48, 48+34, 617)-Net over F64 — Constructive and digital
Digital (48, 82, 617)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 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, 62, 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, 20, 104)-net over F64, using
(48, 48+34, 964)-Net in Base 64 — Constructive
(48, 82, 964)-net in base 64, using
- t-expansion [i] based on (47, 82, 964)-net in base 64, using
- net defined by OOA [i] based on OOA(6482, 964, S64, 35, 35), using
- OOA 17-folding and stacking with additional row [i] based on OA(6482, 16389, S64, 35), using
- discarding factors based on OA(6482, 16390, S64, 35), using
- discarding parts of the base [i] based on linear OA(12870, 16390, F128, 35) (dual of [16390, 16320, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,16]) [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(12865, 16385, F128, 33) (dual of [16385, 16320, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,17]) ⊂ C([0,16]) [i] based on
- discarding parts of the base [i] based on linear OA(12870, 16390, F128, 35) (dual of [16390, 16320, 36]-code), using
- discarding factors based on OA(6482, 16390, S64, 35), using
- OOA 17-folding and stacking with additional row [i] based on OA(6482, 16389, S64, 35), using
- net defined by OOA [i] based on OOA(6482, 964, S64, 35, 35), using
(48, 48+34, 6445)-Net over F64 — Digital
Digital (48, 82, 6445)-net over F64, using
(48, 48+34, large)-Net in Base 64 — Upper bound on s
There is no (48, 82, large)-net in base 64, because
- 32 times m-reduction [i] would yield (48, 50, large)-net in base 64, but