MinT - Best Known (81−37, 81, s)-Nets in Base 5

Best Known (81−37, 81, s)-Nets in Base 5

(81−37, 81, 104)-Net over F₅ — Constructive and digital

Digital (44, 81, 104)-net over F₅, using

1 times m-reduction [i] based on digital (44, 82, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 41, 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]

(81−37, 81, 121)-Net over F₅ — Digital

Digital (44, 81, 121)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(81−37, 81, 2400)-Net in Base 5 — Upper bound on s

There is no (44, 81, 2401)-net in base 5, because

1 times m-reduction [i] would yield (44, 80, 2401)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 83 162516 836687 225392 028037 294131 930464 519559 074973 156825 > 5⁸⁰ [i]