Best Known (209−70, 209, s)-Nets in Base 3
(209−70, 209, 162)-Net over F3 — Constructive and digital
Digital (139, 209, 162)-net over F3, using
- 5 times m-reduction [i] based on digital (139, 214, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 107, 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, 107, 81)-net over F9, using
(209−70, 209, 326)-Net over F3 — Digital
Digital (139, 209, 326)-net over F3, using
(209−70, 209, 4878)-Net in Base 3 — Upper bound on s
There is no (139, 209, 4879)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 5250 358767 103815 392869 739826 869697 137415 550411 075954 653275 070140 943115 483094 122351 991148 453649 332987 > 3209 [i]