Best Known (182, 182+63, s)-Nets in Base 3
(182, 182+63, 324)-Net over F3 — Constructive and digital
Digital (182, 245, 324)-net over F3, using
- 1 times m-reduction [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
(182, 182+63, 903)-Net over F3 — Digital
Digital (182, 245, 903)-net over F3, using
(182, 182+63, 35321)-Net in Base 3 — Upper bound on s
There is no (182, 245, 35322)-net in base 3, because
- 1 times m-reduction [i] would yield (182, 244, 35322)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 261 774880 725337 307770 299419 022493 280583 100292 693073 877033 827237 031530 321983 713726 785559 265010 213345 300392 089179 201945 > 3244 [i]