Best Known (189−60, 189, s)-Nets in Base 3
(189−60, 189, 162)-Net over F3 — Constructive and digital
Digital (129, 189, 162)-net over F3, using
- 5 times m-reduction [i] based on digital (129, 194, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 97, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- trace code for nets [i] based on digital (32, 97, 81)-net over F9, using
(189−60, 189, 354)-Net over F3 — Digital
Digital (129, 189, 354)-net over F3, using
(189−60, 189, 6074)-Net in Base 3 — Upper bound on s
There is no (129, 189, 6075)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 501813 209947 354744 796882 717230 477130 075916 895668 238594 938917 886299 263344 106737 643754 294877 > 3189 [i]