MinT - Best Known (62, 93, s)-Nets in Base 7

Best Known (62, 93, s)-Nets in Base 7

(62, 93, 200)-Net over F₇ — Constructive and digital

Digital (62, 93, 200)-net over F₇, using

7¹ times duplication [i] based on digital (61, 92, 200)-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 (31, 62, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 31, 50)-net over F₄₉, using
      - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(62, 93, 851)-Net over F₇ — Digital

Digital (62, 93, 851)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 93, 163251)-Net in Base 7 — Upper bound on s

There is no (62, 93, 163252)-net in base 7, because

1 times m-reduction [i] would yield (62, 92, 163252)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 561081 400939 653600 921464 350311 700257 632391 222985 243852 341083 343573 280340 398753 > 7⁹² [i]