MinT - Best Known (86, 86+41, s)-Nets in Base 5

Best Known (86, 86+41, s)-Nets in Base 5

(86, 86+41, 296)-Net over F₅ — Constructive and digital

Digital (86, 127, 296)-net over F₅, using

7 times m-reduction [i] based on digital (86, 134, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 67, 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]

(86, 86+41, 672)-Net over F₅ — Digital

Digital (86, 127, 672)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+41, 52557)-Net in Base 5 — Upper bound on s

There is no (86, 127, 52558)-net in base 5, because

1 times m-reduction [i] would yield (86, 126, 52558)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11755 674823 925884 595379 867072 535161 443203 901331 675828 833218 932450 309887 711056 539476 279105 > 5¹²⁶ [i]