Best Known (144, 144+84, s)-Nets in Base 3
(144, 144+84, 156)-Net over F3 — Constructive and digital
Digital (144, 228, 156)-net over F3, using
- 16 times m-reduction [i] based on digital (144, 244, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 122, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- trace code for nets [i] based on digital (22, 122, 78)-net over F9, using
(144, 144+84, 265)-Net over F3 — Digital
Digital (144, 228, 265)-net over F3, using
(144, 144+84, 3171)-Net in Base 3 — Upper bound on s
There is no (144, 228, 3172)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6 129276 631377 705209 322517 145718 044019 477143 282275 720022 220011 760210 832537 675882 905780 499563 496368 373591 466745 > 3228 [i]