MinT - Best Known (62, 88, s)-Nets in Base 7

Best Known (62, 88, s)-Nets in Base 7

(62, 88, 213)-Net over F₇ — Constructive and digital

Digital (62, 88, 213)-net over F₇, using

7¹ times duplication [i] based on digital (61, 87, 213)-net over F₇, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (1, 9, 13)-net over F₇, using
    - 4 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [i]
  2. digital (13, 26, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 13, 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]
  3. digital (26, 52, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 26, 50)-net over F₄₉, using
      - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(62, 88, 1613)-Net over F₇ — Digital

Digital (62, 88, 1613)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 88, 496491)-Net in Base 7 — Upper bound on s

There is no (62, 88, 496492)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 233 688919 263091 472416 429654 222786 753290 903380 627846 481353 992927 415457 970345 > 7⁸⁸ [i]