Best Known (53, 53+78, s)-Nets in Base 3
(53, 53+78, 48)-Net over F3 — Constructive and digital
Digital (53, 131, 48)-net over F3, using
- t-expansion [i] based on digital (45, 131, 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
(53, 53+78, 64)-Net over F3 — Digital
Digital (53, 131, 64)-net over F3, using
- t-expansion [i] based on digital (49, 131, 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
(53, 53+78, 271)-Net in Base 3 — Upper bound on s
There is no (53, 131, 272)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 329 810060 690695 845865 378301 377793 926288 385994 293467 020665 827521 > 3131 [i]