Best Known (196−57, 196, s)-Nets in Base 3
(196−57, 196, 252)-Net over F3 — Constructive and digital
Digital (139, 196, 252)-net over F3, using
- 31 times duplication [i] based on digital (138, 195, 252)-net over F3, using
- trace code for nets [i] based on digital (8, 65, 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
- trace code for nets [i] based on digital (8, 65, 84)-net over F27, using
(196−57, 196, 482)-Net over F3 — Digital
Digital (139, 196, 482)-net over F3, using
(196−57, 196, 11851)-Net in Base 3 — Upper bound on s
There is no (139, 196, 11852)-net in base 3, because
- 1 times m-reduction [i] would yield (139, 195, 11852)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1094 007714 175643 638320 936572 658366 326893 232230 797980 001446 136430 358920 247285 469379 528770 923841 > 3195 [i]