MinT - Best Known (117−74, 117, s)-Nets in Base 5

Best Known (117−74, 117, s)-Nets in Base 5

(117−74, 117, 78)-Net over F₅ — Constructive and digital

Digital (43, 117, 78)-net over F₅, using

t-expansion [i] based on digital (38, 117, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(117−74, 117, 84)-Net over F₅ — Digital

Digital (43, 117, 84)-net over F₅, using

net from sequence [i] based on digital (43, 83)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 43 and N(F) ≥ 84, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(117−74, 117, 567)-Net in Base 5 — Upper bound on s

There is no (43, 117, 568)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6160 140301 470917 561180 278614 482117 170745 678903 020855 086584 465754 575887 246747 991009 > 5¹¹⁷ [i]