Best Known (235−60, 235, s)-Nets in Base 3
(235−60, 235, 324)-Net over F3 — Constructive and digital
Digital (175, 235, 324)-net over F3, using
- 31 times duplication [i] based on digital (174, 234, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 78, 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, 78, 108)-net over F27, using
(235−60, 235, 895)-Net over F3 — Digital
Digital (175, 235, 895)-net over F3, using
(235−60, 235, 32871)-Net in Base 3 — Upper bound on s
There is no (175, 235, 32872)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 13295 551741 159783 366485 261530 371961 974178 611110 543155 021067 043184 686272 789500 273463 014666 824296 700861 287250 989041 > 3235 [i]