MinT - Best Known (89−41, 89, s)-Nets in Base 5

Best Known (89−41, 89, s)-Nets in Base 5

(89−41, 89, 104)-Net over F₅ — Constructive and digital

Digital (48, 89, 104)-net over F₅, using

1 times m-reduction [i] based on digital (48, 90, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 45, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(89−41, 89, 126)-Net over F₅ — Digital

Digital (48, 89, 126)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−41, 89, 2455)-Net in Base 5 — Upper bound on s

There is no (48, 89, 2456)-net in base 5, because

1 times m-reduction [i] would yield (48, 88, 2456)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 32 408917 145953 641248 163687 285977 280166 496296 853634 810149 023745 > 5⁸⁸ [i]