Best Known (109, 232, s)-Nets in Base 3
(109, 232, 74)-Net over F3 — Constructive and digital
Digital (109, 232, 74)-net over F3, using
- t-expansion [i] based on digital (107, 232, 74)-net over F3, using
- net from sequence [i] based on digital (107, 73)-sequence over F3, using
- base reduction for sequences [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- base reduction for sequences [i] based on digital (17, 73)-sequence over F9, using
- net from sequence [i] based on digital (107, 73)-sequence over F3, using
(109, 232, 104)-Net over F3 — Digital
Digital (109, 232, 104)-net over F3, using
- t-expansion [i] based on digital (102, 232, 104)-net over F3, using
- net from sequence [i] based on digital (102, 103)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 102 and N(F) ≥ 104, using
- net from sequence [i] based on digital (102, 103)-sequence over F3, using
(109, 232, 696)-Net in Base 3 — Upper bound on s
There is no (109, 232, 697)-net in base 3, because
- 1 times m-reduction [i] would yield (109, 231, 697)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 170 585188 681946 291944 923658 391047 119926 422523 557927 610689 555083 971605 683281 893298 727395 438358 832570 236192 953475 > 3231 [i]