Best Known (41, 41+42, s)-Nets in Base 3
(41, 41+42, 42)-Net over F3 — Constructive and digital
Digital (41, 83, 42)-net over F3, using
- t-expansion [i] based on digital (39, 83, 42)-net over F3, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 39 and N(F) ≥ 42, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
(41, 41+42, 56)-Net over F3 — Digital
Digital (41, 83, 56)-net over F3, using
- t-expansion [i] based on digital (40, 83, 56)-net over F3, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
(41, 41+42, 313)-Net in Base 3 — Upper bound on s
There is no (41, 83, 314)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 4089 791379 954581 151165 602727 658972 392621 > 383 [i]