Best Known (101−59, 101, s)-Nets in Base 3
(101−59, 101, 42)-Net over F3 — Constructive and digital
Digital (42, 101, 42)-net over F3, using
- t-expansion [i] based on digital (39, 101, 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
(101−59, 101, 56)-Net over F3 — Digital
Digital (42, 101, 56)-net over F3, using
- t-expansion [i] based on digital (40, 101, 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
(101−59, 101, 230)-Net in Base 3 — Upper bound on s
There is no (42, 101, 231)-net in base 3, because
- 1 times m-reduction [i] would yield (42, 100, 231)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 540729 251844 173444 776934 251026 749379 895613 125591 > 3100 [i]