MinT - Best Known (113−33, 113, s)-Nets in Base 5

Best Known (113−33, 113, s)-Nets in Base 5

(113−33, 113, 296)-Net over F₅ — Constructive and digital

Digital (80, 113, 296)-net over F₅, using

9 times m-reduction [i] based on digital (80, 122, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 61, 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]

(113−33, 113, 956)-Net over F₅ — Digital

Digital (80, 113, 956)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−33, 113, 132810)-Net in Base 5 — Upper bound on s

There is no (80, 113, 132811)-net in base 5, because

1 times m-reduction [i] would yield (80, 112, 132811)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 926134 692637 080216 768843 055928 769965 910424 912655 573304 080735 753027 437277 951425 > 5¹¹² [i]