MinT - Best Known (111−31, 111, s)-Nets in Base 5

Best Known (111−31, 111, s)-Nets in Base 5

(111−31, 111, 296)-Net over F₅ — Constructive and digital

Digital (80, 111, 296)-net over F₅, using

11 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]

(111−31, 111, 1176)-Net over F₅ — Digital

Digital (80, 111, 1176)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−31, 111, 214518)-Net in Base 5 — Upper bound on s

There is no (80, 111, 214519)-net in base 5, because

1 times m-reduction [i] would yield (80, 110, 214519)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77039 446296 521654 073782 796007 861056 921868 950045 476593 438575 418502 198890 659109 > 5¹¹⁰ [i]