MinT - Best Known (96, 141, s)-Nets in Base 5

Best Known (96, 141, s)-Nets in Base 5

(96, 141, 400)-Net over F₅ — Constructive and digital

Digital (96, 141, 400)-net over F₅, using

1 times m-reduction [i] based on digital (96, 142, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 71, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(96, 141, 769)-Net over F₅ — Digital

Digital (96, 141, 769)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 141, 63485)-Net in Base 5 — Upper bound on s

There is no (96, 141, 63486)-net in base 5, because

1 times m-reduction [i] would yield (96, 140, 63486)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 758917 430376 830312 241151 574429 293609 536321 205820 519595 944022 890776 044772 487626 566468 594917 477825 > 5¹⁴⁰ [i]