MinT - Best Known (142−37, 142, s)-Nets in Base 5

Best Known (142−37, 142, s)-Nets in Base 5

(142−37, 142, 408)-Net over F₅ — Constructive and digital

Digital (105, 142, 408)-net over F₅, using

8 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]

(142−37, 142, 2058)-Net over F₅ — Digital

Digital (105, 142, 2058)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−37, 142, 564059)-Net in Base 5 — Upper bound on s

There is no (105, 142, 564060)-net in base 5, because

1 times m-reduction [i] would yield (105, 141, 564060)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 358 735571 103974 995413 687234 622849 236663 959498 545264 411569 974696 667241 901156 584552 408416 913732 958785 > 5¹⁴¹ [i]