Best Known (164, 164+55, s)-Nets in Base 3
(164, 164+55, 324)-Net over F3 — Constructive and digital
Digital (164, 219, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 73, 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
(164, 164+55, 899)-Net over F3 — Digital
Digital (164, 219, 899)-net over F3, using
(164, 164+55, 38850)-Net in Base 3 — Upper bound on s
There is no (164, 219, 38851)-net in base 3, because
- 1 times m-reduction [i] would yield (164, 218, 38851)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 102 962653 477157 991790 949978 574484 855235 805270 063654 149075 417588 765851 730315 104055 005869 471086 710772 326139 > 3218 [i]