Best Known (34, 66, s)-Nets in Base 64
(34, 66, 513)-Net over F64 — Constructive and digital
Digital (34, 66, 513)-net over F64, using
- t-expansion [i] based on digital (28, 66, 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, 66, 515)-Net in Base 64 — Constructive
(34, 66, 515)-net in base 64, using
- (u, u+v)-construction [i] based on
- (6, 22, 257)-net in base 64, using
- 2 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
- 2 times m-reduction [i] based on (6, 24, 257)-net in base 64, using
- (12, 44, 258)-net in base 64, using
- base change [i] based on digital (1, 33, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 33, 258)-net over F256, using
- (6, 22, 257)-net in base 64, using
(34, 66, 1780)-Net over F64 — Digital
Digital (34, 66, 1780)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6466, 1780, F64, 2, 32) (dual of [(1780, 2), 3494, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6466, 2053, F64, 2, 32) (dual of [(2053, 2), 4040, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6466, 4106, F64, 32) (dual of [4106, 4040, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(6466, 4107, F64, 32) (dual of [4107, 4041, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- linear OA(6463, 4096, F64, 32) (dual of [4096, 4033, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(6455, 4096, F64, 28) (dual of [4096, 4041, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(6466, 4107, F64, 32) (dual of [4107, 4041, 33]-code), using
- OOA 2-folding [i] based on linear OA(6466, 4106, F64, 32) (dual of [4106, 4040, 33]-code), using
- discarding factors / shortening the dual code based on linear OOA(6466, 2053, F64, 2, 32) (dual of [(2053, 2), 4040, 33]-NRT-code), using
(34, 66, 3045716)-Net in Base 64 — Upper bound on s
There is no (34, 66, 3045717)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 161391 123879 660609 175400 328142 203858 078114 380034 545244 574830 394696 594447 601855 691523 179746 675438 951321 515637 698669 089049 > 6466 [i]