MinT - Best Known (101−55, 101, s)-Nets in Base 7

Best Known (101−55, 101, s)-Nets in Base 7

(101−55, 101, 47)-Net over F₇ — Constructive and digital

Digital (46, 101, 47)-net over F₇, using

net from sequence [i] based on digital (46, 46)-sequence over F₇, using
- base reduction for sequences [i] based on digital (0, 46)-sequence over F₄₉, using
  - s-reduction 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]

(101−55, 101, 110)-Net over F₇ — Digital

Digital (46, 101, 110)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−55, 101, 2438)-Net in Base 7 — Upper bound on s

There is no (46, 101, 2439)-net in base 7, because

1 times m-reduction [i] would yield (46, 100, 2439)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 246853 876106 805815 981503 701299 473350 937047 642437 811239 689319 569433 594888 776130 300191 > 7¹⁰⁰ [i]