MinT - Best Known (135−34, 135, s)-Nets in Base 5

Best Known (135−34, 135, s)-Nets in Base 5

(135−34, 135, 408)-Net over F₅ — Constructive and digital

Digital (101, 135, 408)-net over F₅, using

7 times m-reduction [i] based on digital (101, 142, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 71, 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]

(135−34, 135, 2397)-Net over F₅ — Digital

Digital (101, 135, 2397)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−34, 135, 637559)-Net in Base 5 — Upper bound on s

There is no (101, 135, 637560)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 22958 908885 719166 287036 090457 498989 648579 152825 669554 098984 991142 784998 174688 218177 126505 033185 > 5¹³⁵ [i]