Best Known (51−16, 51, s)-Nets in Base 3
(51−16, 51, 114)-Net over F3 — Constructive and digital
Digital (35, 51, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 17, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
(51−16, 51, 142)-Net over F3 — Digital
Digital (35, 51, 142)-net over F3, using
(51−16, 51, 2064)-Net in Base 3 — Upper bound on s
There is no (35, 51, 2065)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 161009 511260 494388 777377 > 351 [i]