Best Known (85, 85+65, s)-Nets in Base 5
(85, 85+65, 252)-Net over F5 — Constructive and digital
Digital (85, 150, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 75, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(85, 85+65, 5722)-Net in Base 5 — Upper bound on s
There is no (85, 150, 5723)-net in base 5, because
- 1 times m-reduction [i] would yield (85, 149, 5723)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 140 143876 744886 752012 446298 801046 848132 283319 486853 450347 661655 888893 723312 460826 603907 803398 364606 905217 > 5149 [i]