MinT - Best Known (68, 68+27, s)-Nets in Base 5

Best Known (68, 68+27, s)-Nets in Base 5

(68, 68+27, 296)-Net over F₅ — Constructive and digital

Digital (68, 95, 296)-net over F₅, using

3 times m-reduction [i] based on digital (68, 98, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 49, 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]

(68, 68+27, 957)-Net over F₅ — Digital

Digital (68, 95, 957)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+27, 160476)-Net in Base 5 — Upper bound on s

There is no (68, 95, 160477)-net in base 5, because

1 times m-reduction [i] would yield (68, 94, 160477)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 504883 693212 645760 065266 860423 174377 740847 504581 264413 454109 790725 > 5⁹⁴ [i]