Best Known (139−79, 139, s)-Nets in Base 8
(139−79, 139, 99)-Net over F8 — Constructive and digital
Digital (60, 139, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 46, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (14, 93, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (7, 46, 34)-net over F8, using
(139−79, 139, 144)-Net over F8 — Digital
Digital (60, 139, 144)-net over F8, using
- t-expansion [i] based on digital (45, 139, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(139−79, 139, 3425)-Net in Base 8 — Upper bound on s
There is no (60, 139, 3426)-net in base 8, because
- 1 times m-reduction [i] would yield (60, 138, 3426)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 42337 667290 436961 868997 484523 011578 182726 746466 980094 345413 325250 960069 456245 451052 545315 812996 862942 865889 955156 924470 376928 > 8138 [i]