Best Known (162, 162+88, s)-Nets in Base 3
(162, 162+88, 162)-Net over F3 — Constructive and digital
Digital (162, 250, 162)-net over F3, using
- t-expansion [i] based on digital (157, 250, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 125, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- trace code for nets [i] based on digital (32, 125, 81)-net over F9, using
(162, 162+88, 328)-Net over F3 — Digital
Digital (162, 250, 328)-net over F3, using
(162, 162+88, 4390)-Net in Base 3 — Upper bound on s
There is no (162, 250, 4391)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 191038 958679 636621 922185 935308 396962 106177 822024 659289 781133 125830 308229 043170 381388 351806 778545 298850 864420 348125 114025 > 3250 [i]