Best Known (34, 34+26, s)-Nets in Base 64
(34, 34+26, 513)-Net over F64 — Constructive and digital
Digital (34, 60, 513)-net over F64, using
- t-expansion [i] based on digital (28, 60, 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
(34, 34+26, 1260)-Net in Base 64 — Constructive
(34, 60, 1260)-net in base 64, using
- net defined by OOA [i] based on OOA(6460, 1260, S64, 26, 26), using
- OA 13-folding and stacking [i] based on OA(6460, 16380, S64, 26), using
- discarding factors based on OA(6460, 16386, S64, 26), using
- discarding parts of the base [i] based on linear OA(12851, 16386, F128, 26) (dual of [16386, 16335, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(12851, 16384, F128, 26) (dual of [16384, 16333, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(12849, 16384, F128, 25) (dual of [16384, 16335, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 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(25) ⊂ Ce(24) [i] based on
- discarding parts of the base [i] based on linear OA(12851, 16386, F128, 26) (dual of [16386, 16335, 27]-code), using
- discarding factors based on OA(6460, 16386, S64, 26), using
- OA 13-folding and stacking [i] based on OA(6460, 16380, S64, 26), using
(34, 34+26, 4276)-Net over F64 — Digital
Digital (34, 60, 4276)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6460, 4276, F64, 26) (dual of [4276, 4216, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(6460, 4302, F64, 26) (dual of [4302, 4242, 27]-code), using
- 195 step Varšamov–Edel lengthening with (ri) = (5, 0, 0, 1, 7 times 0, 1, 21 times 0, 1, 48 times 0, 1, 112 times 0) [i] based on linear OA(6451, 4098, F64, 26) (dual of [4098, 4047, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(6451, 4096, F64, 26) (dual of [4096, 4045, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(6449, 4096, F64, 25) (dual of [4096, 4047, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(25) ⊂ Ce(24) [i] based on
- 195 step Varšamov–Edel lengthening with (ri) = (5, 0, 0, 1, 7 times 0, 1, 21 times 0, 1, 48 times 0, 1, 112 times 0) [i] based on linear OA(6451, 4098, F64, 26) (dual of [4098, 4047, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(6460, 4302, F64, 26) (dual of [4302, 4242, 27]-code), using
(34, 34+26, large)-Net in Base 64 — Upper bound on s
There is no (34, 60, large)-net in base 64, because
- 24 times m-reduction [i] would yield (34, 36, large)-net in base 64, but