Best Known (163−58, 163, s)-Nets in Base 3
(163−58, 163, 156)-Net over F3 — Constructive and digital
Digital (105, 163, 156)-net over F3, using
- 3 times m-reduction [i] based on digital (105, 166, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 83, 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, 83, 78)-net over F9, using
(163−58, 163, 219)-Net over F3 — Digital
Digital (105, 163, 219)-net over F3, using
(163−58, 163, 2776)-Net in Base 3 — Upper bound on s
There is no (105, 163, 2777)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 595783 924803 989471 995554 564964 701453 896390 248738 243415 550038 869197 743864 277315 > 3163 [i]