Best Known (42, 79, s)-Nets in Base 64
(42, 79, 513)-Net over F64 — Constructive and digital
Digital (42, 79, 513)-net over F64, using
- t-expansion [i] based on digital (28, 79, 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
(42, 79, 545)-Net in Base 64 — Constructive
(42, 79, 545)-net in base 64, using
- 641 times duplication [i] based on (41, 78, 545)-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
- (17, 54, 288)-net in base 64, using
- 2 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
- base change [i] based on digital (9, 48, 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, 48, 288)-net over F128, using
- 2 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
- (6, 24, 257)-net in base 64, using
- (u, u+v)-construction [i] based on
(42, 79, 2323)-Net over F64 — Digital
Digital (42, 79, 2323)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6479, 2323, F64, 37) (dual of [2323, 2244, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(6479, 4116, F64, 37) (dual of [4116, 4037, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(29) [i] based on
- linear OA(6473, 4096, F64, 37) (dual of [4096, 4023, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 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(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(36) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(6479, 4116, F64, 37) (dual of [4116, 4037, 38]-code), using
(42, 79, 8045794)-Net in Base 64 — Upper bound on s
There is no (42, 79, 8045795)-net in base 64, because
- 1 times m-reduction [i] would yield (42, 78, 8045795)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 762 146989 888121 678490 254353 586881 118554 303300 776866 337578 501488 939685 885437 660979 443195 266888 620077 596825 432448 238815 221169 787213 770796 176042 > 6478 [i]