Best Known (46, 46+42, s)-Nets in Base 64
(46, 46+42, 513)-Net over F64 — Constructive and digital
Digital (46, 88, 513)-net over F64, using
- t-expansion [i] based on digital (28, 88, 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
(46, 46+42, 545)-Net in Base 64 — Constructive
(46, 88, 545)-net in base 64, using
- (u, u+v)-construction [i] based on
- (7, 28, 257)-net in base 64, using
- base change [i] based on digital (0, 21, 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, 21, 257)-net over F256, using
- (18, 60, 288)-net in base 64, using
- 3 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on digital (9, 54, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 54, 288)-net over F128, using
- 3 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
- (7, 28, 257)-net in base 64, using
(46, 46+42, 2104)-Net over F64 — Digital
Digital (46, 88, 2104)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6488, 2104, F64, 42) (dual of [2104, 2016, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(6488, 4113, F64, 42) (dual of [4113, 4025, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(35) [i] based on
- linear OA(6483, 4096, F64, 42) (dual of [4096, 4013, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- 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(645, 17, F64, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- construction X applied to Ce(41) ⊂ Ce(35) [i] based on
- discarding factors / shortening the dual code based on linear OA(6488, 4113, F64, 42) (dual of [4113, 4025, 43]-code), using
(46, 46+42, 5103937)-Net in Base 64 — Upper bound on s
There is no (46, 88, 5103938)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 878 697285 568975 340690 765232 068815 922818 302620 095484 472140 225354 403385 305507 453102 229408 706046 851313 690388 181216 977055 050329 344791 899625 419339 264871 632205 096720 > 6488 [i]