MinT - Best Known (43, 86, s)-Nets in Base 7

Best Known (43, 86, s)-Nets in Base 7

(43, 86, 100)-Net over F₇ — Constructive and digital

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]

(43, 86, 134)-Net over F₇ — Digital

Digital (43, 86, 134)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 86, 3796)-Net in Base 7 — Upper bound on s

There is no (43, 86, 3797)-net in base 7, because

1 times m-reduction [i] would yield (43, 85, 3797)-net in base 7, but
- 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]