MinT - Best Known (139−45, 139, s)-Nets in Base 5

Best Known (139−45, 139, s)-Nets in Base 5

(139−45, 139, 296)-Net over F₅ — Constructive and digital

Digital (94, 139, 296)-net over F₅, using

11 times m-reduction [i] based on digital (94, 150, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 75, 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]

(139−45, 139, 711)-Net over F₅ — Digital

Digital (94, 139, 711)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−45, 139, 54842)-Net in Base 5 — Upper bound on s

There is no (94, 139, 54843)-net in base 5, because

1 times m-reduction [i] would yield (94, 138, 54843)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 870823 105603 541937 139518 130543 494477 912959 549877 325652 867486 772402 610294 884001 501917 461830 914985 > 5¹³⁸ [i]