Best Known (163, 163+69, s)-Nets in Base 3
(163, 163+69, 252)-Net over F3 — Constructive and digital
Digital (163, 232, 252)-net over F3, using
- 31 times duplication [i] based on digital (162, 231, 252)-net over F3, using
- trace code for nets [i] based on digital (8, 77, 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, 77, 84)-net over F27, using
(163, 163+69, 519)-Net over F3 — Digital
Digital (163, 232, 519)-net over F3, using
(163, 163+69, 11771)-Net in Base 3 — Upper bound on s
There is no (163, 232, 11772)-net in base 3, because
- 1 times m-reduction [i] would yield (163, 231, 11772)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 164 314072 776742 034665 391489 146230 305539 644942 788325 217963 180488 450386 082784 900546 011967 069384 385305 406125 788681 > 3231 [i]