MinT - Best Known (55−18, 55, s)-Nets in Base 8

Best Known (55−18, 55, s)-Nets in Base 8

(55−18, 55, 354)-Net over F₈ — Constructive and digital

Digital (37, 55, 354)-net over F₈, using

5 times m-reduction [i] based on digital (37, 60, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 30, 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]

(55−18, 55, 518)-Net in Base 8 — Constructive

(37, 55, 518)-net in base 8, using

1 times m-reduction [i] based on (37, 56, 518)-net in base 8, using
- base change [i] based on digital (23, 42, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 21, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(55−18, 55, 865)-Net over F₈ — Digital

Digital (37, 55, 865)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−18, 55, 195670)-Net in Base 8 — Upper bound on s

There is no (37, 55, 195671)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 46 769539 206473 884903 205940 519446 670736 500149 005556 > 8⁵⁵ [i]