MinT - Best Known (62−20, 62, s)-Nets in Base 7

Best Known (62−20, 62, s)-Nets in Base 7

(62−20, 62, 202)-Net over F₇ — Constructive and digital

Digital (42, 62, 202)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (10, 20, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 10, 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]
2. digital (22, 42, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 21, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(62−20, 62, 766)-Net over F₇ — Digital

Digital (42, 62, 766)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(62−20, 62, 131042)-Net in Base 7 — Upper bound on s

There is no (42, 62, 131043)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 24893 852050 060328 142869 549050 114146 606366 243205 302349 > 7⁶² [i]