MinT - Best Known (110−36, 110, s)-Nets in Base 7

Best Known (110−36, 110, s)-Nets in Base 7

(110−36, 110, 202)-Net over F₇ — Constructive and digital

Digital (74, 110, 202)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (18, 36, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 18, 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 (38, 74, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 37, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(110−36, 110, 1067)-Net over F₇ — Digital

Digital (74, 110, 1067)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−36, 110, 183839)-Net in Base 7 — Upper bound on s

There is no (74, 110, 183840)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 913 672749 283045 267233 847838 807809 184885 551678 012583 887483 654503 647491 221671 739928 625367 909313 > 7¹¹⁰ [i]