Best Known (46, 46+36, s)-Nets in Base 64
(46, 46+36, 578)-Net over F64 — Constructive and digital
Digital (46, 82, 578)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 18, 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 (28, 64, 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
- digital (0, 18, 65)-net over F64, using
(46, 46+36, 4300)-Net over F64 — Digital
Digital (46, 82, 4300)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6482, 4300, F64, 36) (dual of [4300, 4218, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(6482, 4323, F64, 36) (dual of [4323, 4241, 37]-code), using
- 214 step Varšamov–Edel lengthening with (ri) = (6, 0, 0, 1, 4 times 0, 1, 13 times 0, 1, 26 times 0, 1, 55 times 0, 1, 108 times 0) [i] based on linear OA(6471, 4098, F64, 36) (dual of [4098, 4027, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- linear OA(6471, 4096, F64, 36) (dual of [4096, 4025, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(6469, 4096, F64, 35) (dual of [4096, 4027, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- 214 step Varšamov–Edel lengthening with (ri) = (6, 0, 0, 1, 4 times 0, 1, 13 times 0, 1, 26 times 0, 1, 55 times 0, 1, 108 times 0) [i] based on linear OA(6471, 4098, F64, 36) (dual of [4098, 4027, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(6482, 4323, F64, 36) (dual of [4323, 4241, 37]-code), using
(46, 46+36, large)-Net in Base 64 — Upper bound on s
There is no (46, 82, large)-net in base 64, because
- 34 times m-reduction [i] would yield (46, 48, large)-net in base 64, but