MinT - Best Known (148−40, 148, s)-Nets in Base 5

Best Known (148−40, 148, s)-Nets in Base 5

(148−40, 148, 408)-Net over F₅ — Constructive and digital

Digital (108, 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]

(148−40, 148, 1749)-Net over F₅ — Digital

Digital (108, 148, 1749)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−40, 148, 308747)-Net in Base 5 — Upper bound on s

There is no (108, 148, 308748)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 026326 455901 433046 450568 980713 527107 235766 045166 826753 893011 938702 620391 516841 154845 787778 618045 402881 > 5¹⁴⁸ [i]