MinT - Best Known (100, 100+61, s)-Nets in Base 8

Best Known (100, 100+61, s)-Nets in Base 8

(100, 100+61, 354)-Net over F₈ — Constructive and digital

Digital (100, 161, 354)-net over F₈, using

t-expansion [i] based on digital (93, 161, 354)-net over F₈, using
- 11 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(100, 100+61, 432)-Net in Base 8 — Constructive

(100, 161, 432)-net in base 8, using

5 times m-reduction [i] based on (100, 166, 432)-net in base 8, using
- trace code for nets [i] based on (17, 83, 216)-net in base 64, using
  - 1 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
    - base change [i] based on digital (5, 72, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(100, 100+61, 884)-Net over F₈ — Digital

Digital (100, 161, 884)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+61, 112745)-Net in Base 8 — Upper bound on s

There is no (100, 161, 112746)-net in base 8, because

1 times m-reduction [i] would yield (100, 160, 112746)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 122381 629642 763959 272534 992653 481127 608772 629851 716918 157329 007378 808914 477266 317562 841882 809422 316607 032858 769045 229635 675974 434125 538401 419056 > 8¹⁶⁰ [i]