MinT - Best Known (107, 107+39, s)-Nets in Base 5

Best Known (107, 107+39, s)-Nets in Base 5

(107, 107+39, 408)-Net over F₅ — Constructive and digital

Digital (107, 146, 408)-net over F₅, using

t-expansion [i] based on digital (105, 146, 408)-net over F₅, using
- 4 times m-reduction [i] based on digital (105, 150, 408)-net over F₅, using
  - trace code for nets [i] based on digital (30, 75, 204)-net over F₂₅, using
    - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
        a function field by GarcÃa and Quoos [i]

(107, 107+39, 1840)-Net over F₅ — Digital

Digital (107, 146, 1840)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+39, 427943)-Net in Base 5 — Upper bound on s

There is no (107, 146, 427944)-net in base 5, because

1 times m-reduction [i] would yield (107, 145, 427944)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224213 741628 471548 310721 190240 404413 577589 321555 842262 761919 555498 420962 937824 457092 591551 477133 501345 > 5¹⁴⁵ [i]