Best Known (148−91, 148, s)-Nets in Base 3
(148−91, 148, 48)-Net over F3 — Constructive and digital
Digital (57, 148, 48)-net over F3, using
- t-expansion [i] based on digital (45, 148, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(148−91, 148, 64)-Net over F3 — Digital
Digital (57, 148, 64)-net over F3, using
- t-expansion [i] based on digital (49, 148, 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
(148−91, 148, 276)-Net in Base 3 — Upper bound on s
There is no (57, 148, 277)-net in base 3, because
- 1 times m-reduction [i] would yield (57, 147, 277)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 13957 876487 680766 937289 269514 370703 141206 823849 764752 669207 097744 558235 > 3147 [i]