MinT - Best Known (107, 107+41, s)-Nets in Base 5

Best Known (107, 107+41, s)-Nets in Base 5

(107, 107+41, 408)-Net over F₅ — Constructive and digital

Digital (107, 148, 408)-net over F₅, using

t-expansion [i] based on digital (105, 148, 408)-net over F₅, using
- 2 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+41, 1540)-Net over F₅ — Digital

Digital (107, 148, 1540)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+41, 284874)-Net in Base 5 — Upper bound on s

There is no (107, 148, 284875)-net in base 5, because

1 times m-reduction [i] would yield (107, 147, 284875)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 605367 119342 449344 516283 967652 799826 227583 516763 708500 291920 659754 713371 458716 953661 892052 584673 470001 > 5¹⁴⁷ [i]