Best Known (55, 110, s)-Nets in Base 3
(55, 110, 52)-Net over F3 — Constructive and digital
Digital (55, 110, 52)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 40, 24)-net over F3, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 13 and N(F) ≥ 24, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- digital (15, 70, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- digital (13, 40, 24)-net over F3, using
(55, 110, 64)-Net over F3 — Digital
Digital (55, 110, 64)-net over F3, using
- t-expansion [i] based on digital (49, 110, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(55, 110, 434)-Net in Base 3 — Upper bound on s
There is no (55, 110, 435)-net in base 3, because
- 1 times m-reduction [i] would yield (55, 109, 435)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 10180 404418 109919 213645 419543 578041 380706 786537 452987 > 3109 [i]