MinT - Best Known (52, 52+51, s)-Nets in Base 7

Best Known (52, 52+51, s)-Nets in Base 7

(52, 52+51, 100)-Net over F₇ — Constructive and digital

Digital (52, 103, 100)-net over F₇, using

1 times m-reduction [i] based on digital (52, 104, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 52, 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]

(52, 52+51, 160)-Net over F₇ — Digital

Digital (52, 103, 160)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+51, 4742)-Net in Base 7 — Upper bound on s

There is no (52, 103, 4743)-net in base 7, because

1 times m-reduction [i] would yield (52, 102, 4743)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 158 989362 241976 063286 566258 125661 952131 785652 712734 516166 723372 221371 932655 807877 824411 > 7¹⁰² [i]