Best Known (144, 144+64, s)-Nets in Base 3
(144, 144+64, 204)-Net over F3 — Constructive and digital
Digital (144, 208, 204)-net over F3, using
- 31 times duplication [i] based on digital (143, 207, 204)-net over F3, using
- trace code for nets [i] based on digital (5, 69, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- trace code for nets [i] based on digital (5, 69, 68)-net over F27, using
(144, 144+64, 423)-Net over F3 — Digital
Digital (144, 208, 423)-net over F3, using
(144, 144+64, 8043)-Net in Base 3 — Upper bound on s
There is no (144, 208, 8044)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1746 310385 977806 907640 986614 641330 822111 437980 891427 639348 807462 932260 301647 494377 412057 325033 064705 > 3208 [i]