MinT - Best Known (111−45, 111, s)-Nets in Base 5

Best Known (111−45, 111, s)-Nets in Base 5

(111−45, 111, 252)-Net over F₅ — Constructive and digital

Digital (66, 111, 252)-net over F₅, using

1 times m-reduction [i] based on digital (66, 112, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 56, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(111−45, 111, 7057)-Net in Base 5 — Upper bound on s

There is no (66, 111, 7058)-net in base 5, because

1 times m-reduction [i] would yield (66, 110, 7058)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77119 966345 722318 582130 315508 403884 782077 753603 497854 869816 771282 027364 104705 > 5¹¹⁰ [i]