MinT - Best Known (107−32, 107, s)-Nets in Base 5

Best Known (107−32, 107, s)-Nets in Base 5

(107−32, 107, 296)-Net over F₅ — Constructive and digital

Digital (75, 107, 296)-net over F₅, using

5 times m-reduction [i] based on digital (75, 112, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 56, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(107−32, 107, 818)-Net over F₅ — Digital

Digital (75, 107, 818)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−32, 107, 80311)-Net in Base 5 — Upper bound on s

There is no (75, 107, 80312)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 616 342620 920460 350156 923850 631550 387082 200046 631829 280738 740581 642149 894145 > 5¹⁰⁷ [i]