Best Known (35, 69, s)-Nets in Base 64
(35, 69, 513)-Net over F64 — Constructive and digital
Digital (35, 69, 513)-net over F64, using
- t-expansion [i] based on digital (28, 69, 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
(35, 69, 514)-Net in Base 64 — Constructive
(35, 69, 514)-net in base 64, using
- 1 times m-reduction [i] based on (35, 70, 514)-net in base 64, using
- (u, u+v)-construction [i] based on
- (6, 23, 257)-net in base 64, using
- 1 times m-reduction [i] based on (6, 24, 257)-net in base 64, using
- base change [i] based on digital (0, 18, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 18, 257)-net over F256, using
- 1 times m-reduction [i] based on (6, 24, 257)-net in base 64, using
- (12, 47, 257)-net in base 64, using
- 1 times m-reduction [i] based on (12, 48, 257)-net in base 64, using
- base change [i] based on digital (0, 36, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- base change [i] based on digital (0, 36, 257)-net over F256, using
- 1 times m-reduction [i] based on (12, 48, 257)-net in base 64, using
- (6, 23, 257)-net in base 64, using
- (u, u+v)-construction [i] based on
(35, 69, 1564)-Net over F64 — Digital
Digital (35, 69, 1564)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6469, 1564, F64, 2, 34) (dual of [(1564, 2), 3059, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6469, 2052, F64, 2, 34) (dual of [(2052, 2), 4035, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6469, 4104, F64, 34) (dual of [4104, 4035, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- linear OA(6467, 4096, F64, 34) (dual of [4096, 4029, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(6461, 4096, F64, 31) (dual of [4096, 4035, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(642, 8, F64, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- OOA 2-folding [i] based on linear OA(6469, 4104, F64, 34) (dual of [4104, 4035, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(6469, 2052, F64, 2, 34) (dual of [(2052, 2), 4035, 35]-NRT-code), using
(35, 69, 2441006)-Net in Base 64 — Upper bound on s
There is no (35, 69, 2441007)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 42307 684825 348473 294330 007346 594871 725588 396771 081990 495713 336597 215624 419108 519406 474495 814318 160330 828150 683154 674682 057140 > 6469 [i]