Best Known (123, 123+52, s)-Nets in Base 3
(123, 123+52, 228)-Net over F3 — Constructive and digital
Digital (123, 175, 228)-net over F3, using
- 31 times duplication [i] based on digital (122, 174, 228)-net over F3, using
- trace code for nets [i] based on digital (6, 58, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- trace code for nets [i] based on digital (6, 58, 76)-net over F27, using
(123, 123+52, 408)-Net over F3 — Digital
Digital (123, 175, 408)-net over F3, using
(123, 123+52, 8557)-Net in Base 3 — Upper bound on s
There is no (123, 175, 8558)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 313612 930400 020512 064812 778097 739935 897589 141631 387062 393089 774105 611172 356005 680589 > 3175 [i]