MinT - Best Known (107−47, 107, s)-Nets in Base 5

Best Known (107−47, 107, s)-Nets in Base 5

(107−47, 107, 132)-Net over F₅ — Constructive and digital

Digital (60, 107, 132)-net over F₅, using

5 times m-reduction [i] based on digital (60, 112, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 56, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(107−47, 107, 172)-Net over F₅ — Digital

Digital (60, 107, 172)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−47, 107, 3907)-Net in Base 5 — Upper bound on s

There is no (60, 107, 3908)-net in base 5, because

1 times m-reduction [i] would yield (60, 106, 3908)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 123 735959 215148 402295 997738 338789 566000 677536 091468 629512 284473 413896 673425 > 5¹⁰⁶ [i]