MinT - Best Known (67, 67+25, s)-Nets in Base 5

Best Known (67, 67+25, s)-Nets in Base 5

(67, 67+25, 296)-Net over F₅ — Constructive and digital

Digital (67, 92, 296)-net over F₅, using

4 times m-reduction [i] based on digital (67, 96, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 48, 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]

(67, 67+25, 1183)-Net over F₅ — Digital

Digital (67, 92, 1183)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+25, 264125)-Net in Base 5 — Upper bound on s

There is no (67, 92, 264126)-net in base 5, because

1 times m-reduction [i] would yield (67, 91, 264126)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4039 098969 136261 595226 756318 425308 893861 110273 110852 398336 242625 > 5⁹¹ [i]