Best Known (207−68, 207, s)-Nets in Base 3
(207−68, 207, 162)-Net over F3 — Constructive and digital
Digital (139, 207, 162)-net over F3, using
- 7 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
(207−68, 207, 343)-Net over F3 — Digital
Digital (139, 207, 343)-net over F3, using
(207−68, 207, 5402)-Net in Base 3 — Upper bound on s
There is no (139, 207, 5403)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 582 748484 093938 456115 466347 874249 053681 840973 492208 550646 670491 571254 780319 010148 568429 769097 103125 > 3207 [i]