MinT - Best Known (120−39, 120, s)-Nets in Base 5

Best Known (120−39, 120, s)-Nets in Base 5

(120−39, 120, 296)-Net over F₅ — Constructive and digital

Digital (81, 120, 296)-net over F₅, using

4 times m-reduction [i] based on digital (81, 124, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 62, 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]

(120−39, 120, 624)-Net over F₅ — Digital

Digital (81, 120, 624)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−39, 120, 47292)-Net in Base 5 — Upper bound on s

There is no (81, 120, 47293)-net in base 5, because

1 times m-reduction [i] would yield (81, 119, 47293)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 150516 497898 597033 789767 875867 455867 609102 527252 888376 327273 722229 248873 888944 722925 > 5¹¹⁹ [i]