Best Known (78−32, 78, s)-Nets in Base 64
(78−32, 78, 593)-Net over F64 — Constructive and digital
Digital (46, 78, 593)-net over F64, using
- 2 times m-reduction [i] based on digital (46, 80, 593)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 18, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (28, 62, 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
- digital (1, 18, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(78−32, 78, 1024)-Net in Base 64 — Constructive
(46, 78, 1024)-net in base 64, using
- 641 times duplication [i] based on (45, 77, 1024)-net in base 64, using
- t-expansion [i] based on (44, 77, 1024)-net in base 64, using
- base change [i] based on digital (33, 66, 1024)-net over F128, using
- 1281 times duplication [i] based on digital (32, 65, 1024)-net over F128, using
- net defined by OOA [i] based on linear OOA(12865, 1024, F128, 33, 33) (dual of [(1024, 33), 33727, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(12865, 16385, F128, 33) (dual of [16385, 16320, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- OOA 16-folding and stacking with additional row [i] based on linear OA(12865, 16385, F128, 33) (dual of [16385, 16320, 34]-code), using
- net defined by OOA [i] based on linear OOA(12865, 1024, F128, 33, 33) (dual of [(1024, 33), 33727, 34]-NRT-code), using
- 1281 times duplication [i] based on digital (32, 65, 1024)-net over F128, using
- base change [i] based on digital (33, 66, 1024)-net over F128, using
- t-expansion [i] based on (44, 77, 1024)-net in base 64, using
(78−32, 78, 6922)-Net over F64 — Digital
Digital (46, 78, 6922)-net over F64, using
(78−32, 78, large)-Net in Base 64 — Upper bound on s
There is no (46, 78, large)-net in base 64, because
- 30 times m-reduction [i] would yield (46, 48, large)-net in base 64, but