Best Known (101−53, 101, s)-Nets in Base 3
(101−53, 101, 48)-Net over F3 — Constructive and digital
Digital (48, 101, 48)-net over F3, using
- t-expansion [i] based on digital (45, 101, 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
(101−53, 101, 56)-Net over F3 — Digital
Digital (48, 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
(101−53, 101, 336)-Net in Base 3 — Upper bound on s
There is no (48, 101, 337)-net in base 3, because
- 1 times m-reduction [i] would yield (48, 100, 337)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 550310 660238 758830 059717 399491 385651 851579 375625 > 3100 [i]