MinT - Best Known (50, 50+49, s)-Nets in Base 7

Best Known (50, 50+49, s)-Nets in Base 7

(50, 50+49, 100)-Net over F₇ — Constructive and digital

Digital (50, 99, 100)-net over F₇, using

1 times m-reduction [i] based on digital (50, 100, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 50, 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]

(50, 50+49, 156)-Net over F₇ — Digital

Digital (50, 99, 156)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+49, 4597)-Net in Base 7 — Upper bound on s

There is no (50, 99, 4598)-net in base 7, because

1 times m-reduction [i] would yield (50, 98, 4598)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 66011 405501 217411 919329 177071 052632 291103 043557 784613 730446 450969 846919 669521 349169 > 7⁹⁸ [i]