MinT - Best Known (109−35, 109, s)-Nets in Base 5

Best Known (109−35, 109, s)-Nets in Base 5

(109−35, 109, 296)-Net over F₅ — Constructive and digital

Digital (74, 109, 296)-net over F₅, using

1 times m-reduction [i] based on digital (74, 110, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 55, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(109−35, 109, 606)-Net over F₅ — Digital

Digital (74, 109, 606)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−35, 109, 49464)-Net in Base 5 — Upper bound on s

There is no (74, 109, 49465)-net in base 5, because

1 times m-reduction [i] would yield (74, 108, 49465)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3082 091836 283717 796416 199207 630778 581082 249904 723801 516786 758147 421352 078245 > 5¹⁰⁸ [i]