MinT - Best Known (85, 85+31, s)-Nets in Base 5

Best Known (85, 85+31, s)-Nets in Base 5

(85, 85+31, 400)-Net over F₅ — Constructive and digital

Digital (85, 116, 400)-net over F₅, using

4 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+31, 1533)-Net over F₅ — Digital

Digital (85, 116, 1533)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+31, 366829)-Net in Base 5 — Upper bound on s

There is no (85, 116, 366830)-net in base 5, because

1 times m-reduction [i] would yield (85, 115, 366830)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 240 748642 517795 286613 564643 049339 333582 283095 561531 867977 186698 504658 363794 832345 > 5¹¹⁵ [i]