MinT - Best Known (89−29, 89, s)-Nets in Base 7

Best Known (89−29, 89, s)-Nets in Base 7

(89−29, 89, 202)-Net over F₇ — Constructive and digital

Digital (60, 89, 202)-net over F₇, using

7¹ times duplication [i] based on digital (59, 88, 202)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 28, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 14, 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 (31, 60, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 30, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]

(89−29, 89, 928)-Net over F₇ — Digital

Digital (60, 89, 928)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−29, 89, 206696)-Net in Base 7 — Upper bound on s

There is no (60, 89, 206697)-net in base 7, because

1 times m-reduction [i] would yield (60, 88, 206697)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 233 693917 393078 799008 201531 156965 652538 407583 193015 819190 883534 251496 235553 > 7⁸⁸ [i]