MinT - Best Known (69, 103, s)-Nets in Base 7

Best Known (69, 103, s)-Nets in Base 7

(69, 103, 200)-Net over F₇ — Constructive and digital

Digital (69, 103, 200)-net over F₇, using

1 times m-reduction [i] based on digital (69, 104, 200)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (17, 34, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 17, 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 (35, 70, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 35, 50)-net over F₄₉, using
      - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(69, 103, 969)-Net over F₇ — Digital

Digital (69, 103, 969)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 103, 157784)-Net in Base 7 — Upper bound on s

There is no (69, 103, 157785)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1109 498608 633877 249646 253480 653070 734243 526122 543383 423080 673257 767047 241961 272484 886935 > 7¹⁰³ [i]