MinT - Best Known (126−43, 126, s)-Nets in Base 5

Best Known (126−43, 126, s)-Nets in Base 5

(126−43, 126, 296)-Net over F₅ — Constructive and digital

Digital (83, 126, 296)-net over F₅, using

2 times m-reduction [i] based on digital (83, 128, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 64, 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]

(126−43, 126, 520)-Net over F₅ — Digital

Digital (83, 126, 520)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−43, 126, 31387)-Net in Base 5 — Upper bound on s

There is no (83, 126, 31388)-net in base 5, because

1 times m-reduction [i] would yield (83, 125, 31388)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2351 698590 069947 921547 893368 050434 583004 904731 927374 833289 587364 323324 019421 186794 167025 > 5¹²⁵ [i]