Best Known (38, 38+35, s)-Nets in Base 3
(38, 38+35, 42)-Net over F3 — Constructive and digital
Digital (38, 73, 42)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (6, 23, 14)-net over F3, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 6 and N(F) ≥ 14, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- digital (15, 50, 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 (6, 23, 14)-net over F3, using
(38, 38+35, 52)-Net over F3 — Digital
Digital (38, 73, 52)-net over F3, using
- t-expansion [i] based on digital (37, 73, 52)-net over F3, using
- net from sequence [i] based on digital (37, 51)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 37 and N(F) ≥ 52, using
- net from sequence [i] based on digital (37, 51)-sequence over F3, using
(38, 38+35, 360)-Net in Base 3 — Upper bound on s
There is no (38, 73, 361)-net in base 3, because
- 1 times m-reduction [i] would yield (38, 72, 361)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 23348 095072 369960 758150 345053 782419 > 372 [i]