MinT - Best Known (129−43, 129, s)-Nets in Base 5

Best Known (129−43, 129, s)-Nets in Base 5

(129−43, 129, 296)-Net over F₅ — Constructive and digital

Digital (86, 129, 296)-net over F₅, using

5 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]

(129−43, 129, 588)-Net over F₅ — Digital

Digital (86, 129, 588)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−43, 129, 39505)-Net in Base 5 — Upper bound on s

There is no (86, 129, 39506)-net in base 5, because

1 times m-reduction [i] would yield (86, 128, 39506)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 294008 260887 212667 422500 798380 423915 499319 205521 922183 541799 160508 515356 902631 520088 919625 > 5¹²⁸ [i]