Best Known (111−29, 111, s)-Nets in Base 3
(111−29, 111, 252)-Net over F3 — Constructive and digital
Digital (82, 111, 252)-net over F3, using
- trace code for nets [i] based on digital (8, 37, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
(111−29, 111, 454)-Net over F3 — Digital
Digital (82, 111, 454)-net over F3, using
(111−29, 111, 16939)-Net in Base 3 — Upper bound on s
There is no (82, 111, 16940)-net in base 3, because
- 1 times m-reduction [i] would yield (82, 110, 16940)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 30453 776826 413459 557286 075280 393233 443388 595956 912457 > 3110 [i]