MinT - Best Known (18, 18+18, s)-Nets in Base 5

Best Known (18, 18+18, s)-Nets in Base 5

(18, 18+18, 52)-Net over F₅ — Constructive and digital

Digital (18, 36, 52)-net over F₅, using

trace code for nets [i] based on digital (0, 18, 26)-net over F₂₅, using
- net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
    - the rational function field F₂₅(x) [i]
  - Niederreiter sequence [i]

(18, 18+18, 641)-Net in Base 5 — Upper bound on s

There is no (18, 36, 642)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 599047 729840 465012 165385 > 5³⁶ [i]