Best Known (37, 37+36, s)-Nets in Base 64
(37, 37+36, 513)-Net over F64 — Constructive and digital
Digital (37, 73, 513)-net over F64, using
- t-expansion [i] based on digital (28, 73, 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
(37, 37+36, 514)-Net in Base 64 — Constructive
(37, 73, 514)-net in base 64, using
- 1 times m-reduction [i] based on (37, 74, 514)-net in base 64, using
- (u, u+v)-construction [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
- (13, 50, 257)-net in base 64, using
- 2 times m-reduction [i] based on (13, 52, 257)-net in base 64, using
- base change [i] based on digital (0, 39, 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, 39, 257)-net over F256, using
- 2 times m-reduction [i] based on (13, 52, 257)-net in base 64, using
- (6, 24, 257)-net in base 64, using
- (u, u+v)-construction [i] based on
(37, 37+36, 1591)-Net over F64 — Digital
Digital (37, 73, 1591)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6473, 1591, F64, 2, 36) (dual of [(1591, 2), 3109, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6473, 2052, F64, 2, 36) (dual of [(2052, 2), 4031, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6473, 4104, F64, 36) (dual of [4104, 4031, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(32) [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(6465, 4096, F64, 33) (dual of [4096, 4031, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(35) ⊂ Ce(32) [i] based on
- OOA 2-folding [i] based on linear OA(6473, 4104, F64, 36) (dual of [4104, 4031, 37]-code), using
- discarding factors / shortening the dual code based on linear OOA(6473, 2052, F64, 2, 36) (dual of [(2052, 2), 4031, 37]-NRT-code), using
(37, 37+36, 2534260)-Net in Base 64 — Upper bound on s
There is no (37, 73, 2534261)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 709806 700711 907153 934248 118360 054700 265215 811899 715399 302392 269044 566724 147000 461192 536700 544646 628909 074736 794100 227761 355875 614490 > 6473 [i]