Best Known (99, 154, s)-Nets in Base 3
(99, 154, 156)-Net over F3 — Constructive and digital
Digital (99, 154, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 77, 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
(99, 154, 207)-Net over F3 — Digital
Digital (99, 154, 207)-net over F3, using
(99, 154, 2734)-Net in Base 3 — Upper bound on s
There is no (99, 154, 2735)-net in base 3, because
- 1 times m-reduction [i] would yield (99, 153, 2735)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 10 029847 785600 266007 784272 462871 783298 330061 476730 136326 432180 225085 758091 > 3153 [i]