MinT - Best Known (135−59, 135, s)-Nets in Base 5

Best Known (135−59, 135, s)-Nets in Base 5

(135−59, 135, 132)-Net over F₅ — Constructive and digital

Digital (76, 135, 132)-net over F₅, using

9 times m-reduction [i] based on digital (76, 144, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 72, 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]

(135−59, 135, 212)-Net over F₅ — Digital

Digital (76, 135, 212)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−59, 135, 4930)-Net in Base 5 — Upper bound on s

There is no (76, 135, 4931)-net in base 5, because

1 times m-reduction [i] would yield (76, 134, 4931)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4596 129256 831935 209755 521843 947720 820342 989494 523296 126585 943508 822916 482783 766160 082003 716765 > 5¹³⁴ [i]