MinT - Best Known (148−47, 148, s)-Nets in Base 5

Best Known (148−47, 148, s)-Nets in Base 5

(148−47, 148, 400)-Net over F₅ — Constructive and digital

Digital (101, 148, 400)-net over F₅, using

t-expansion [i] based on digital (100, 148, 400)-net over F₅, using
- 2 times m-reduction [i] based on digital (100, 150, 400)-net over F₅, using
  - trace code for nets [i] based on digital (25, 75, 200)-net over F₂₅, using
    - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
        a function field by GarcÃa and Quoos [i]

(148−47, 148, 817)-Net over F₅ — Digital

Digital (101, 148, 817)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−47, 148, 69122)-Net in Base 5 — Upper bound on s

There is no (101, 148, 69123)-net in base 5, because

1 times m-reduction [i] would yield (101, 147, 69123)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 605633 148960 833326 843080 731576 707203 668836 821625 477641 141297 530580 717145 442094 636491 816221 310452 789365 > 5¹⁴⁷ [i]