Best Known (49, 49+56, s)-Nets in Base 8
(49, 49+56, 99)-Net over F8 — Constructive and digital
Digital (49, 105, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 35, 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, 70, 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, 35, 34)-net over F8, using
(49, 49+56, 144)-Net over F8 — Digital
Digital (49, 105, 144)-net over F8, using
- t-expansion [i] based on digital (45, 105, 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
(49, 49+56, 3913)-Net in Base 8 — Upper bound on s
There is no (49, 105, 3914)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 67013 462043 149342 908092 272998 596070 074439 237834 160274 702458 020499 941222 617849 963581 511285 356400 > 8105 [i]