Best Known (61, 83, s)-Nets in Base 64
(61, 83, 24026)-Net over F64 — Constructive and digital
Digital (61, 83, 24026)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (8, 19, 195)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 3, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- digital (0, 5, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 11, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 3, 65)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (42, 64, 23831)-net over F64, using
- net defined by OOA [i] based on linear OOA(6464, 23831, F64, 22, 22) (dual of [(23831, 22), 524218, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(6464, 262141, F64, 22) (dual of [262141, 262077, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(6464, 262141, F64, 22) (dual of [262141, 262077, 23]-code), using
- net defined by OOA [i] based on linear OOA(6464, 23831, F64, 22, 22) (dual of [(23831, 22), 524218, 23]-NRT-code), using
- digital (8, 19, 195)-net over F64, using
(61, 83, 190653)-Net in Base 64 — Constructive
(61, 83, 190653)-net in base 64, using
- net defined by OOA [i] based on OOA(6483, 190653, S64, 22, 22), using
- OA 11-folding and stacking [i] based on OA(6483, 2097183, S64, 22), using
- discarding parts of the base [i] based on linear OA(12871, 2097183, F128, 22) (dual of [2097183, 2097112, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-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 Ce(21) ⊂ Ce(13) [i] based on
- discarding parts of the base [i] based on linear OA(12871, 2097183, F128, 22) (dual of [2097183, 2097112, 23]-code), using
- OA 11-folding and stacking [i] based on OA(6483, 2097183, S64, 22), using
(61, 83, 1896120)-Net over F64 — Digital
Digital (61, 83, 1896120)-net over F64, using
(61, 83, large)-Net in Base 64 — Upper bound on s
There is no (61, 83, large)-net in base 64, because
- 20 times m-reduction [i] would yield (61, 63, large)-net in base 64, but