Best Known (247−64, 247, s)-Nets in Base 3
(247−64, 247, 324)-Net over F3 — Constructive and digital
Digital (183, 247, 324)-net over F3, using
- 31 times duplication [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
(247−64, 247, 883)-Net over F3 — Digital
Digital (183, 247, 883)-net over F3, using
(247−64, 247, 30774)-Net in Base 3 — Upper bound on s
There is no (183, 247, 30775)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 7068 667644 836999 688013 915369 065869 183925 868069 962506 280990 078645 086124 908554 297098 849961 634456 577968 457492 082209 148353 > 3247 [i]