Best Known (174, 174+59, s)-Nets in Base 3
(174, 174+59, 324)-Net over F3 — Constructive and digital
Digital (174, 233, 324)-net over F3, using
- 1 times m-reduction [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
(174, 174+59, 917)-Net over F3 — Digital
Digital (174, 233, 917)-net over F3, using
(174, 174+59, 38259)-Net in Base 3 — Upper bound on s
There is no (174, 233, 38260)-net in base 3, because
- 1 times m-reduction [i] would yield (174, 232, 38260)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 492 391293 921442 559557 804023 291789 089210 795034 008554 817509 848212 711659 534545 225657 367740 663071 474117 033963 694153 > 3232 [i]