Best Known (144, 144+58, s)-Nets in Base 3
(144, 144+58, 264)-Net over F3 — Constructive and digital
Digital (144, 202, 264)-net over F3, using
- 31 times duplication [i] based on digital (143, 201, 264)-net over F3, using
- trace code for nets [i] based on digital (9, 67, 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, 67, 88)-net over F27, using
(144, 144+58, 516)-Net over F3 — Digital
Digital (144, 202, 516)-net over F3, using
(144, 144+58, 12259)-Net in Base 3 — Upper bound on s
There is no (144, 202, 12260)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 392049 245054 684016 321024 793965 978895 645390 547811 375010 020712 590222 156525 083830 341205 419698 508073 > 3202 [i]