MinT - Best Known (97−45, 97, s)-Nets in Base 5

Best Known (97−45, 97, s)-Nets in Base 5

(97−45, 97, 104)-Net over F₅ — Constructive and digital

Digital (52, 97, 104)-net over F₅, using

1 times m-reduction [i] based on digital (52, 98, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 49, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(97−45, 97, 131)-Net over F₅ — Digital

Digital (52, 97, 131)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−45, 97, 2524)-Net in Base 5 — Upper bound on s

There is no (52, 97, 2525)-net in base 5, because

1 times m-reduction [i] would yield (52, 96, 2525)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12 720953 369893 791012 176367 663569 938437 850596 435899 917827 471428 995401 > 5⁹⁶ [i]