MinT - Best Known (127−42, 127, s)-Nets in Base 5

Best Known (127−42, 127, s)-Nets in Base 5

(127−42, 127, 296)-Net over F₅ — Constructive and digital

Digital (85, 127, 296)-net over F₅, using

5 times m-reduction [i] based on digital (85, 132, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 66, 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]

(127−42, 127, 602)-Net over F₅ — Digital

Digital (85, 127, 602)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−42, 127, 36589)-Net in Base 5 — Upper bound on s

There is no (85, 127, 36590)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 58793 086134 312840 841303 259838 108122 581550 880378 795388 404000 598747 962208 853374 622383 630905 > 5¹²⁷ [i]