Best Known (83, 83+60, s)-Nets in Base 5
(83, 83+60, 252)-Net over F5 — Constructive and digital
Digital (83, 143, 252)-net over F5, using
- 3 times m-reduction [i] based on digital (83, 146, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 73, 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
- trace code for nets [i] based on digital (10, 73, 126)-net over F25, using
(83, 83+60, 258)-Net over F5 — Digital
Digital (83, 143, 258)-net over F5, using
(83, 83+60, 6441)-Net in Base 5 — Upper bound on s
There is no (83, 143, 6442)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 8976 894494 383819 430285 502883 389905 335989 760044 819646 689950 335575 330844 507732 617386 438190 826848 892161 > 5143 [i]