Best Known (55−21, 55, s)-Nets in Base 64
(55−21, 55, 520)-Net over F64 — Constructive and digital
Digital (34, 55, 520)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 65)-net over F64, using
- 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, 3, 65)-net over F64 (see above)
- 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, 7, 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, 21, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
(55−21, 55, 6553)-Net in Base 64 — Constructive
(34, 55, 6553)-net in base 64, using
- net defined by OOA [i] based on OOA(6455, 6553, S64, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(6455, 65531, S64, 21), using
- discarding factors based on OA(6455, 65538, S64, 21), using
- discarding parts of the base [i] based on linear OA(25641, 65538, F256, 21) (dual of [65538, 65497, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(25641, 65538, F256, 21) (dual of [65538, 65497, 22]-code), using
- discarding factors based on OA(6455, 65538, S64, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(6455, 65531, S64, 21), using
(55−21, 55, 12227)-Net over F64 — Digital
Digital (34, 55, 12227)-net over F64, using
(55−21, 55, large)-Net in Base 64 — Upper bound on s
There is no (34, 55, large)-net in base 64, because
- 19 times m-reduction [i] would yield (34, 36, large)-net in base 64, but