MinT - Best Known (34, 74, s)-Nets in Base 5

Best Known (34, 74, s)-Nets in Base 5

(34, 74, 72)-Net over F₅ — Constructive and digital

Digital (34, 74, 72)-net over F₅, using

t-expansion [i] based on digital (31, 74, 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, 74, 76)-Net over F₅ — Digital

Digital (34, 74, 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, 74, 786)-Net in Base 5 — Upper bound on s

There is no (34, 74, 787)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5396 682213 247494 385784 167094 380885 615840 713432 020785 > 5⁷⁴ [i]