MinT - Best Known (102−42, 102, s)-Nets in Base 8

Best Known (102−42, 102, s)-Nets in Base 8

(102−42, 102, 354)-Net over F₈ — Constructive and digital

Digital (60, 102, 354)-net over F₈, using

4 times m-reduction [i] based on digital (60, 106, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 53, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(102−42, 102, 418)-Net over F₈ — Digital

Digital (60, 102, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 51, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(102−42, 102, 30174)-Net in Base 8 — Upper bound on s

There is no (60, 102, 30175)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 130 387383 355167 550120 275661 880095 630654 903972 537238 371132 943083 696376 681399 444131 912885 898306 > 8¹⁰² [i]