Best Known (73−34, 73, s)-Nets in Base 64
(73−34, 73, 513)-Net over F64 — Constructive and digital
Digital (39, 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
(73−34, 73, 517)-Net in Base 64 — Constructive
(39, 73, 517)-net in base 64, using
- 1 times m-reduction [i] based on (39, 74, 517)-net in base 64, using
- (u, u+v)-construction [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
- (15, 50, 259)-net in base 64, using
- 2 times m-reduction [i] based on (15, 52, 259)-net in base 64, using
- base change [i] based on digital (2, 39, 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, 39, 259)-net over F256, using
- 2 times m-reduction [i] based on (15, 52, 259)-net in base 64, using
- (7, 24, 258)-net in base 64, using
- (u, u+v)-construction [i] based on
(73−34, 73, 2337)-Net over F64 — Digital
Digital (39, 73, 2337)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6473, 2337, F64, 34) (dual of [2337, 2264, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(6473, 4116, F64, 34) (dual of [4116, 4043, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(26) [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(6453, 4096, F64, 27) (dual of [4096, 4043, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(33) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(6473, 4116, F64, 34) (dual of [4116, 4043, 35]-code), using
(73−34, 73, 6494614)-Net in Base 64 — Upper bound on s
There is no (39, 73, 6494615)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 709803 632896 157749 346330 451098 029910 615439 591054 382617 941797 184430 387369 713145 723037 994075 088430 384186 638188 724513 149338 203149 412850 > 6473 [i]