MinT - Best Known (86, 86+39, s)-Nets in Base 5

Best Known (86, 86+39, s)-Nets in Base 5

(86, 86+39, 296)-Net over F₅ — Constructive and digital

Digital (86, 125, 296)-net over F₅, using

9 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+39, 767)-Net over F₅ — Digital

Digital (86, 125, 767)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+39, 72239)-Net in Base 5 — Upper bound on s

There is no (86, 125, 72240)-net in base 5, because

1 times m-reduction [i] would yield (86, 124, 72240)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 470 319034 213569 598420 904268 079455 151361 157835 886788 061583 131215 502286 218337 463685 857985 > 5¹²⁴ [i]