MinT - Best Known (141−37, 141, s)-Nets in Base 5

Best Known (141−37, 141, s)-Nets in Base 5

(141−37, 141, 408)-Net over F₅ — Constructive and digital

Digital (104, 141, 408)-net over F₅, using

7 times m-reduction [i] based on digital (104, 148, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 74, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(141−37, 141, 1969)-Net over F₅ — Digital

Digital (104, 141, 1969)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−37, 141, 515813)-Net in Base 5 — Upper bound on s

There is no (104, 141, 515814)-net in base 5, because

1 times m-reduction [i] would yield (104, 140, 515814)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 748379 232425 799085 491733 988561 645036 062019 551207 857917 266318 695456 305168 361465 650279 719611 401345 > 5¹⁴⁰ [i]