Best Known (23, 38, s)-Nets in Base 64
(23, 38, 665)-Net over F64 — Constructive and digital
Digital (23, 38, 665)-net over F64, using
- 641 times duplication [i] based on digital (22, 37, 665)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (14, 29, 585)-net over F64, using
- net defined by OOA [i] based on linear OOA(6429, 585, F64, 15, 15) (dual of [(585, 15), 8746, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6429, 4096, F64, 15) (dual of [4096, 4067, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(6429, 4096, F64, 15) (dual of [4096, 4067, 16]-code), using
- net defined by OOA [i] based on linear OOA(6429, 585, F64, 15, 15) (dual of [(585, 15), 8746, 16]-NRT-code), using
- digital (1, 8, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(23, 38, 2342)-Net in Base 64 — Constructive
(23, 38, 2342)-net in base 64, using
- net defined by OOA [i] based on OOA(6438, 2342, S64, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(6438, 16395, S64, 15), using
- discarding factors based on OA(6438, 16396, S64, 15), using
- discarding parts of the base [i] based on linear OA(12832, 16396, F128, 15) (dual of [16396, 16364, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- linear OA(12829, 16385, F128, 15) (dual of [16385, 16356, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(12821, 16385, F128, 11) (dual of [16385, 16364, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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([0,7]) ⊂ C([0,5]) [i] based on
- discarding parts of the base [i] based on linear OA(12832, 16396, F128, 15) (dual of [16396, 16364, 16]-code), using
- discarding factors based on OA(6438, 16396, S64, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(6438, 16395, S64, 15), using
(23, 38, 7674)-Net over F64 — Digital
Digital (23, 38, 7674)-net over F64, using
(23, 38, large)-Net in Base 64 — Upper bound on s
There is no (23, 38, large)-net in base 64, because
- 13 times m-reduction [i] would yield (23, 25, large)-net in base 64, but