Best Known (137−73, 137, s)-Nets in Base 3
(137−73, 137, 52)-Net over F3 — Constructive and digital
Digital (64, 137, 52)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 49, 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, 88, 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, 49, 24)-net over F3, using
(137−73, 137, 64)-Net over F3 — Digital
Digital (64, 137, 64)-net over F3, using
- t-expansion [i] based on digital (49, 137, 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
(137−73, 137, 418)-Net in Base 3 — Upper bound on s
There is no (64, 137, 419)-net in base 3, because
- 1 times m-reduction [i] would yield (64, 136, 419)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 79330 532483 601979 323335 103289 652699 542976 248052 777615 058959 957145 > 3136 [i]