Best Known (18, 18+8, s)-Nets in Base 64
(18, 18+8, 65601)-Net over F64 — Constructive and digital
Digital (18, 26, 65601)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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 (14, 22, 65536)-net over F64, using
- net defined by OOA [i] based on linear OOA(6422, 65536, F64, 8, 8) (dual of [(65536, 8), 524266, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using
- net defined by OOA [i] based on linear OOA(6422, 65536, F64, 8, 8) (dual of [(65536, 8), 524266, 9]-NRT-code), using
- digital (0, 4, 65)-net over F64, using
(18, 18+8, 274317)-Net over F64 — Digital
Digital (18, 26, 274317)-net over F64, using
(18, 18+8, 524288)-Net in Base 64 — Constructive
(18, 26, 524288)-net in base 64, using
- net defined by OOA [i] based on OOA(6426, 524288, S64, 8, 8), using
- OA 4-folding and stacking [i] based on OA(6426, 2097152, S64, 8), using
- discarding factors based on OA(6426, 2097155, S64, 8), using
- discarding parts of the base [i] based on linear OA(12822, 2097155, F128, 8) (dual of [2097155, 2097133, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding parts of the base [i] based on linear OA(12822, 2097155, F128, 8) (dual of [2097155, 2097133, 9]-code), using
- discarding factors based on OA(6426, 2097155, S64, 8), using
- OA 4-folding and stacking [i] based on OA(6426, 2097152, S64, 8), using
(18, 18+8, large)-Net in Base 64 — Upper bound on s
There is no (18, 26, large)-net in base 64, because
- 6 times m-reduction [i] would yield (18, 20, large)-net in base 64, but