Best Known (180, 180+61, s)-Nets in Base 3
(180, 180+61, 324)-Net over F3 — Constructive and digital
Digital (180, 241, 324)-net over F3, using
- 2 times m-reduction [i] based on digital (180, 243, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 81, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- trace code for nets [i] based on digital (18, 81, 108)-net over F27, using
(180, 180+61, 945)-Net over F3 — Digital
Digital (180, 241, 945)-net over F3, using
(180, 180+61, 39482)-Net in Base 3 — Upper bound on s
There is no (180, 241, 39483)-net in base 3, because
- 1 times m-reduction [i] would yield (180, 240, 39483)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 3 230516 968109 758907 541714 597004 535990 662858 635726 660108 843132 759333 144510 999434 380633 219462 132918 020364 885691 178845 > 3240 [i]