Best Known (117−40, 117, s)-Nets in Base 5
(117−40, 117, 252)-Net over F5 — Constructive and digital
Digital (77, 117, 252)-net over F5, using
- 17 times m-reduction [i] based on digital (77, 134, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 67, 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, 67, 126)-net over F25, using
(117−40, 117, 487)-Net over F5 — Digital
Digital (77, 117, 487)-net over F5, using
(117−40, 117, 25466)-Net in Base 5 — Upper bound on s
There is no (77, 117, 25467)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 6019 688067 301678 264608 433547 964044 782294 894856 505667 010219 891357 044822 832115 803185 > 5117 [i]