MinT - Best Known (85, 85+45, s)-Nets in Base 5

Best Known (85, 85+45, s)-Nets in Base 5

(85, 85+45, 296)-Net over F₅ — Constructive and digital

Digital (85, 130, 296)-net over F₅, using

2 times m-reduction [i] based on digital (85, 132, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 66, 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]

(85, 85+45, 501)-Net over F₅ — Digital

Digital (85, 130, 501)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+45, 28382)-Net in Base 5 — Upper bound on s

There is no (85, 130, 28383)-net in base 5, because

1 times m-reduction [i] would yield (85, 129, 28383)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 469667 780612 675636 410471 210074 967085 602238 202620 322501 745823 773734 726105 404277 276791 002025 > 5¹²⁹ [i]