Best Known (178−50, 178, s)-Nets in Base 3
(178−50, 178, 264)-Net over F3 — Constructive and digital
Digital (128, 178, 264)-net over F3, using
- 31 times duplication [i] based on digital (127, 177, 264)-net over F3, using
- trace code for nets [i] based on digital (9, 59, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- trace code for nets [i] based on digital (9, 59, 88)-net over F27, using
(178−50, 178, 500)-Net over F3 — Digital
Digital (128, 178, 500)-net over F3, using
(178−50, 178, 12672)-Net in Base 3 — Upper bound on s
There is no (128, 178, 12673)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 8 473110 410269 296986 671413 401729 575314 211591 724569 090782 061244 543735 566245 088219 411875 > 3178 [i]