Best Known (235−59, 235, s)-Nets in Base 3
(235−59, 235, 324)-Net over F3 — Constructive and digital
Digital (176, 235, 324)-net over F3, using
- 2 times m-reduction [i] based on digital (176, 237, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 79, 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, 79, 108)-net over F27, using
(235−59, 235, 955)-Net over F3 — Digital
Digital (176, 235, 955)-net over F3, using
(235−59, 235, 41273)-Net in Base 3 — Upper bound on s
There is no (176, 235, 41274)-net in base 3, because
- 1 times m-reduction [i] would yield (176, 234, 41274)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 4432 435298 841336 626871 886677 356992 828884 250582 172175 562337 119959 159054 000189 499538 269147 516704 331687 528301 192669 > 3234 [i]