MinT - Best Known (105−45, 105, s)-Nets in Base 5

Best Known (105−45, 105, s)-Nets in Base 5

(105−45, 105, 132)-Net over F₅ — Constructive and digital

Digital (60, 105, 132)-net over F₅, using

7 times m-reduction [i] based on digital (60, 112, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 56, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(105−45, 105, 186)-Net over F₅ — Digital

Digital (60, 105, 186)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−45, 105, 4544)-Net in Base 5 — Upper bound on s

There is no (60, 105, 4545)-net in base 5, because

1 times m-reduction [i] would yield (60, 104, 4545)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 941200 538425 113567 145268 799260 656452 778183 705328 481560 073665 268646 623945 > 5¹⁰⁴ [i]