Best Known (212−74, 212, s)-Nets in Base 3
(212−74, 212, 162)-Net over F3 — Constructive and digital
Digital (138, 212, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 106, 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
(212−74, 212, 291)-Net over F3 — Digital
Digital (138, 212, 291)-net over F3, using
(212−74, 212, 3932)-Net in Base 3 — Upper bound on s
There is no (138, 212, 3933)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 141916 606789 052942 293399 927831 621325 069865 805384 525548 574740 444918 341543 517565 958391 714184 994647 896139 > 3212 [i]