Best Known (125, 125+74, s)-Nets in Base 3
(125, 125+74, 156)-Net over F3 — Constructive and digital
Digital (125, 199, 156)-net over F3, using
- 7 times m-reduction [i] based on digital (125, 206, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 103, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- trace code for nets [i] based on digital (22, 103, 78)-net over F9, using
(125, 125+74, 229)-Net over F3 — Digital
Digital (125, 199, 229)-net over F3, using
(125, 125+74, 2661)-Net in Base 3 — Upper bound on s
There is no (125, 199, 2662)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 89060 235840 089534 272334 858243 401990 126512 572042 520033 838455 399933 551108 762166 838791 129416 691045 > 3199 [i]