MinT - Best Known (90−25, 90, s)-Nets in Base 5

Best Known (90−25, 90, s)-Nets in Base 5

(90−25, 90, 296)-Net over F₅ — Constructive and digital

Digital (65, 90, 296)-net over F₅, using

2 times m-reduction [i] based on digital (65, 92, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 46, 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]

(90−25, 90, 1036)-Net over F₅ — Digital

Digital (65, 90, 1036)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−25, 90, 201981)-Net in Base 5 — Upper bound on s

There is no (65, 90, 201982)-net in base 5, because

1 times m-reduction [i] would yield (65, 89, 201982)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 161 567594 550846 422518 892968 955837 463469 544839 941484 702309 106625 > 5⁸⁹ [i]