Best Known (243−61, 243, s)-Nets in Base 3
(243−61, 243, 324)-Net over F3 — Constructive and digital
Digital (182, 243, 324)-net over F3, using
- 3 times m-reduction [i] based on digital (182, 246, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 82, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- trace code for nets [i] based on digital (18, 82, 108)-net over F27, using
(243−61, 243, 983)-Net over F3 — Digital
Digital (182, 243, 983)-net over F3, using
(243−61, 243, 42484)-Net in Base 3 — Upper bound on s
There is no (182, 243, 42485)-net in base 3, because
- 1 times m-reduction [i] would yield (182, 242, 42485)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 29 063602 792605 796177 927108 820820 913986 157192 792690 043503 569693 273060 451377 839625 853633 698776 351373 563017 174852 671745 > 3242 [i]