Best Known (38, 62, s)-Nets in Base 64
(38, 62, 513)-Net over F64 — Constructive and digital
Digital (38, 62, 513)-net over F64, using
- t-expansion [i] based on 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
(38, 62, 1367)-Net in Base 64 — Constructive
(38, 62, 1367)-net in base 64, using
- net defined by OOA [i] based on OOA(6462, 1367, S64, 24, 24), using
- OA 12-folding and stacking [i] based on OA(6462, 16404, S64, 24), using
- discarding parts of the base [i] based on linear OA(12853, 16404, F128, 24) (dual of [16404, 16351, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(12833, 16384, F128, 17) (dual of [16384, 16351, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1286, 20, F128, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,128)), using
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- Reed–Solomon code RS(122,128) [i]
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- discarding parts of the base [i] based on linear OA(12853, 16404, F128, 24) (dual of [16404, 16351, 25]-code), using
- OA 12-folding and stacking [i] based on OA(6462, 16404, S64, 24), using
(38, 62, 11076)-Net over F64 — Digital
Digital (38, 62, 11076)-net over F64, using
(38, 62, large)-Net in Base 64 — Upper bound on s
There is no (38, 62, large)-net in base 64, because
- 22 times m-reduction [i] would yield (38, 40, large)-net in base 64, but