Best Known (228−82, 228, s)-Nets in Base 3
(228−82, 228, 162)-Net over F3 — Constructive and digital
Digital (146, 228, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 114, 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
(228−82, 228, 284)-Net over F3 — Digital
Digital (146, 228, 284)-net over F3, using
(228−82, 228, 3591)-Net in Base 3 — Upper bound on s
There is no (146, 228, 3592)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6 099761 724438 964552 611877 049779 724626 548006 513167 608434 279954 487608 464223 158131 508206 483058 739533 056723 938705 > 3228 [i]