Best Known (227−138, 227, s)-Nets in Base 3
(227−138, 227, 64)-Net over F3 — Constructive and digital
Digital (89, 227, 64)-net over F3, using
- net from sequence [i] based on digital (89, 63)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
(227−138, 227, 96)-Net over F3 — Digital
Digital (89, 227, 96)-net over F3, using
- net from sequence [i] based on digital (89, 95)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 89 and N(F) ≥ 96, using
(227−138, 227, 427)-Net in Base 3 — Upper bound on s
There is no (89, 227, 428)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 151678 204823 712711 493613 576534 500948 225208 608771 252506 817471 816232 124206 847381 762054 374485 344379 369102 019641 > 3227 [i]