Best Known (233−78, 233, s)-Nets in Base 3
(233−78, 233, 162)-Net over F3 — Constructive and digital
Digital (155, 233, 162)-net over F3, using
- 13 times m-reduction [i] based on digital (155, 246, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 123, 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, 123, 81)-net over F9, using
(233−78, 233, 358)-Net over F3 — Digital
Digital (155, 233, 358)-net over F3, using
(233−78, 233, 5417)-Net in Base 3 — Upper bound on s
There is no (155, 233, 5418)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1478 720863 719785 122029 677416 580570 324397 601119 424457 626784 155963 857199 921188 367538 014274 040363 983279 075661 067145 > 3233 [i]