Best Known (170, 170+57, s)-Nets in Base 3
(170, 170+57, 324)-Net over F3 — Constructive and digital
Digital (170, 227, 324)-net over F3, using
- 1 times m-reduction [i] based on digital (170, 228, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 76, 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, 76, 108)-net over F27, using
(170, 170+57, 927)-Net over F3 — Digital
Digital (170, 227, 927)-net over F3, using
(170, 170+57, 40061)-Net in Base 3 — Upper bound on s
There is no (170, 227, 40062)-net in base 3, because
- 1 times m-reduction [i] would yield (170, 226, 40062)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 675389 924570 883474 067484 108984 031348 352057 507944 377806 635150 492456 090172 448116 100652 151079 703933 163195 008377 > 3226 [i]