MinT - Best Known (95−31, 95, s)-Nets in Base 7

Best Known (95−31, 95, s)-Nets in Base 7

(95−31, 95, 202)-Net over F₇ — Constructive and digital

Digital (64, 95, 202)-net over F₇, using

7¹ times duplication [i] based on digital (63, 94, 202)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 30, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 15, 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 (33, 64, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 32, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]

(95−31, 95, 967)-Net over F₇ — Digital

Digital (64, 95, 967)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−31, 95, 211613)-Net in Base 7 — Upper bound on s

There is no (64, 95, 211614)-net in base 7, because

1 times m-reduction [i] would yield (64, 94, 211614)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 27 493341 885206 484083 808382 079519 676832 053426 806136 144522 720892 315106 820150 715153 > 7⁹⁴ [i]