Best Known (139, 139+42, s)-Nets in Base 3
(139, 139+42, 464)-Net over F3 — Constructive and digital
Digital (139, 181, 464)-net over F3, using
- 31 times duplication [i] based on digital (138, 180, 464)-net over F3, using
- t-expansion [i] based on digital (137, 180, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 45, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 45, 116)-net over F81, using
- t-expansion [i] based on digital (137, 180, 464)-net over F3, using
(139, 139+42, 1051)-Net over F3 — Digital
Digital (139, 181, 1051)-net over F3, using
(139, 139+42, 56186)-Net in Base 3 — Upper bound on s
There is no (139, 181, 56187)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 228 541536 059014 494005 574568 369626 176385 158210 930547 948650 208003 066205 630975 797039 669775 > 3181 [i]