Best Known (34, 34+20, s)-Nets in Base 64
(34, 34+20, 585)-Net over F64 — Constructive and digital
Digital (34, 54, 585)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 65)-net over F64, using
- digital (0, 2, 65)-net over F64 (see above)
- digital (0, 2, 65)-net over F64 (see above)
- 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, 4, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 5, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 6, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 10, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 20, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
(34, 34+20, 6554)-Net in Base 64 — Constructive
(34, 54, 6554)-net in base 64, using
- net defined by OOA [i] based on OOA(6454, 6554, S64, 20, 20), using
- OA 10-folding and stacking [i] based on OA(6454, 65540, S64, 20), using
- discarding factors based on OA(6454, 65541, S64, 20), using
- discarding parts of the base [i] based on linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- discarding parts of the base [i] based on linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- discarding factors based on OA(6454, 65541, S64, 20), using
- OA 10-folding and stacking [i] based on OA(6454, 65540, S64, 20), using
(34, 34+20, 17119)-Net over F64 — Digital
Digital (34, 54, 17119)-net over F64, using
(34, 34+20, large)-Net in Base 64 — Upper bound on s
There is no (34, 54, large)-net in base 64, because
- 18 times m-reduction [i] would yield (34, 36, large)-net in base 64, but