MinT - Best Known (85, 85+37, s)-Nets in Base 5

Best Known (85, 85+37, s)-Nets in Base 5

(85, 85+37, 296)-Net over F₅ — Constructive and digital

Digital (85, 122, 296)-net over F₅, using

10 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+37, 852)-Net over F₅ — Digital

Digital (85, 122, 852)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+37, 94328)-Net in Base 5 — Upper bound on s

There is no (85, 122, 94329)-net in base 5, because

1 times m-reduction [i] would yield (85, 121, 94329)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 762098 728812 012375 596545 589231 229991 813434 005329 131493 736840 451441 692711 111086 386905 > 5¹²¹ [i]