MinT - Best Known (85, 85+33, s)-Nets in Base 5

Best Known (85, 85+33, s)-Nets in Base 5

(85, 85+33, 400)-Net over F₅ — Constructive and digital

Digital (85, 118, 400)-net over F₅, using

2 times m-reduction [i] based on digital (85, 120, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 60, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(85, 85+33, 1224)-Net over F₅ — Digital

Digital (85, 118, 1224)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+33, 219621)-Net in Base 5 — Upper bound on s

There is no (85, 118, 219622)-net in base 5, because

1 times m-reduction [i] would yield (85, 117, 219622)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6018 906248 644665 053723 870687 692373 461909 609387 766573 653115 612153 136170 558884 726529 > 5¹¹⁷ [i]