Best Known (180−54, 180, s)-Nets in Base 3
(180−54, 180, 228)-Net over F3 — Constructive and digital
Digital (126, 180, 228)-net over F3, using
- trace code for nets [i] based on digital (6, 60, 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
(180−54, 180, 405)-Net over F3 — Digital
Digital (126, 180, 405)-net over F3, using
(180−54, 180, 8256)-Net in Base 3 — Upper bound on s
There is no (126, 180, 8257)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 76 304768 430926 437412 514776 018753 912462 905402 545486 406435 218672 806867 808728 687110 596283 > 3180 [i]