Best Known (144, 244, s)-Nets in Base 3
(144, 244, 156)-Net over F3 — Constructive and digital
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
(144, 244, 208)-Net over F3 — Digital
Digital (144, 244, 208)-net over F3, using
(144, 244, 2025)-Net in Base 3 — Upper bound on s
There is no (144, 244, 2026)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 262 708159 659793 763445 052710 385207 767012 995551 365180 823664 984616 609917 356329 178325 381733 258550 210098 001149 308107 952421 > 3244 [i]