MinT - Best Known (85−24, 85, s)-Nets in Base 3

Best Known (85−24, 85, s)-Nets in Base 3

(85−24, 85, 192)-Net over F₃ — Constructive and digital

Digital (61, 85, 192)-net over F₃, using

3¹ times duplication [i] based on digital (60, 84, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 28, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(85−24, 85, 282)-Net over F₃ — Digital

Digital (61, 85, 282)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−24, 85, 6326)-Net in Base 3 — Upper bound on s

There is no (61, 85, 6327)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35962 819458 941614 797934 123584 043948 462569 > 3⁸⁵ [i]