MinT - Best Known (34, 34+60, s)-Nets in Base 5

Best Known (34, 34+60, s)-Nets in Base 5

(34, 34+60, 72)-Net over F₅ — Constructive and digital

Digital (34, 94, 72)-net over F₅, using

t-expansion [i] based on digital (31, 94, 72)-net over F₅, using
- net from sequence [i] based on digital (31, 71)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
    - an explicitly constructive algebraic function field [i]

(34, 34+60, 76)-Net over F₅ — Digital

Digital (34, 94, 76)-net over F₅, using

net from sequence [i] based on digital (34, 75)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 34 and N(F) ≥ 76, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(34, 34+60, 444)-Net in Base 5 — Upper bound on s

There is no (34, 94, 445)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 509928 230015 177376 891740 026528 815073 576623 358263 561446 146637 605161 > 5⁹⁴ [i]