Best Known (29, 29+17, s)-Nets in Base 5
(29, 29+17, 132)-Net over F5 — Constructive and digital
Digital (29, 46, 132)-net over F5, using
- 4 times m-reduction [i] based on digital (29, 50, 132)-net over F5, using
- trace code for nets [i] based on digital (4, 25, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- trace code for nets [i] based on digital (4, 25, 66)-net over F25, using
(29, 29+17, 182)-Net over F5 — Digital
Digital (29, 46, 182)-net over F5, using
(29, 29+17, 8035)-Net in Base 5 — Upper bound on s
There is no (29, 46, 8036)-net in base 5, because
- 1 times m-reduction [i] would yield (29, 45, 8036)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 28 422045 244297 745310 203567 033345 > 545 [i]