MinT - Best Known (109−62, 109, s)-Nets in Base 5

Best Known (109−62, 109, s)-Nets in Base 5

(109−62, 109, 78)-Net over F₅ — Constructive and digital

Digital (47, 109, 78)-net over F₅, using

t-expansion [i] based on digital (38, 109, 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]

(109−62, 109, 92)-Net over F₅ — Digital

Digital (47, 109, 92)-net over F₅, using

net from sequence [i] based on digital (47, 91)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 47 and N(F) ≥ 92, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(109−62, 109, 867)-Net in Base 5 — Upper bound on s

There is no (47, 109, 868)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 15422 773126 225524 641484 198178 814693 684396 690293 676868 774890 078942 621925 597201 > 5¹⁰⁹ [i]