Best Known (162−50, 162, s)-Nets in Base 3
(162−50, 162, 192)-Net over F3 — Constructive and digital
Digital (112, 162, 192)-net over F3, using
- trace code for nets [i] based on digital (4, 54, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
(162−50, 162, 338)-Net over F3 — Digital
Digital (112, 162, 338)-net over F3, using
(162−50, 162, 6261)-Net in Base 3 — Upper bound on s
There is no (112, 162, 6262)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 197359 666345 228669 895918 489970 106738 901295 466997 356066 124455 736467 917388 831293 > 3162 [i]