Best Known (35, 65, s)-Nets in Base 64
(35, 65, 513)-Net over F64 — Constructive and digital
Digital (35, 65, 513)-net over F64, using
- t-expansion [i] based on digital (28, 65, 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, 65, 517)-Net in Base 64 — Constructive
(35, 65, 517)-net in base 64, using
- 1 times m-reduction [i] based on (35, 66, 517)-net in base 64, using
- (u, u+v)-construction [i] based on
- (7, 22, 258)-net in base 64, using
- 2 times m-reduction [i] based on (7, 24, 258)-net in base 64, using
- base change [i] based on digital (1, 18, 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, 18, 258)-net over F256, using
- 2 times m-reduction [i] based on (7, 24, 258)-net in base 64, using
- (13, 44, 259)-net in base 64, using
- base change [i] based on digital (2, 33, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 33, 259)-net over F256, using
- (7, 22, 258)-net in base 64, using
- (u, u+v)-construction [i] based on
(35, 65, 2397)-Net over F64 — Digital
Digital (35, 65, 2397)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6465, 2397, F64, 30) (dual of [2397, 2332, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(6465, 4116, F64, 30) (dual of [4116, 4051, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- linear OA(6459, 4096, F64, 30) (dual of [4096, 4037, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(6445, 4096, F64, 23) (dual of [4096, 4051, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(646, 20, F64, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(6465, 4116, F64, 30) (dual of [4116, 4051, 31]-code), using
(35, 65, 6842353)-Net in Base 64 — Upper bound on s
There is no (35, 65, 6842354)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 2521 730156 177206 759395 817229 814505 889826 377144 448457 386142 479118 257752 145385 207969 401676 078343 430257 436173 315721 868264 > 6465 [i]