Best Known (182, 182+64, s)-Nets in Base 3
(182, 182+64, 324)-Net over F3 — Constructive and digital
Digital (182, 246, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 82, 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
(182, 182+64, 867)-Net over F3 — Digital
Digital (182, 246, 867)-net over F3, using
(182, 182+64, 29734)-Net in Base 3 — Upper bound on s
There is no (182, 246, 29735)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2355 430719 605190 871776 377569 032910 840611 777835 948388 524383 879860 560028 765019 471652 273751 477026 838455 173011 779185 258945 > 3246 [i]