MinT - Best Known (85−42, 85, s)-Nets in Base 7

Best Known (85−42, 85, s)-Nets in Base 7

(85−42, 85, 100)-Net over F₇ — Constructive and digital

Digital (43, 85, 100)-net over F₇, using

1 times m-reduction [i] based on digital (43, 86, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 43, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
      - the rational function field F₄₉(x) [i]
    - Niederreiter sequence [i]

(85−42, 85, 139)-Net over F₇ — Digital

Digital (43, 85, 139)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−42, 85, 3796)-Net in Base 7 — Upper bound on s

There is no (43, 85, 3797)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 681422 586416 415000 733010 822479 543282 811660 798176 490134 483716 693115 958143 > 7⁸⁵ [i]