MinT - Best Known (101−39, 101, s)-Nets in Base 8

Best Known (101−39, 101, s)-Nets in Base 8

(101−39, 101, 354)-Net over F₈ — Constructive and digital

Digital (62, 101, 354)-net over F₈, using

9 times m-reduction [i] based on digital (62, 110, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 55, 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]

(101−39, 101, 384)-Net in Base 8 — Constructive

(62, 101, 384)-net in base 8, using

1 times m-reduction [i] based on (62, 102, 384)-net in base 8, using
- trace code for nets [i] based on (11, 51, 192)-net in base 64, using
  - 5 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
    - base change [i] based on digital (3, 48, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(101−39, 101, 558)-Net over F₈ — Digital

Digital (62, 101, 558)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−39, 101, 64142)-Net in Base 8 — Upper bound on s

There is no (62, 101, 64143)-net in base 8, because

1 times m-reduction [i] would yield (62, 100, 64143)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 037562 698325 368356 810475 108818 022044 269860 431381 455836 079133 174439 065249 563786 497067 835360 > 8¹⁰⁰ [i]