MinT - Best Known (76, 126, s)-Nets in Base 8

Best Known (76, 126, s)-Nets in Base 8

(76, 126, 354)-Net over F₈ — Constructive and digital

Digital (76, 126, 354)-net over F₈, using

12 times m-reduction [i] based on digital (76, 138, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 69, 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]

(76, 126, 384)-Net in Base 8 — Constructive

(76, 126, 384)-net in base 8, using

t-expansion [i] based on (75, 126, 384)-net in base 8, using
- trace code for nets [i] based on (12, 63, 192)-net in base 64, using
  - base change [i] based on digital (3, 54, 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]

(76, 126, 576)-Net over F₈ — Digital

Digital (76, 126, 576)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 126, 51757)-Net in Base 8 — Upper bound on s

There is no (76, 126, 51758)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 615897 054983 048430 692235 053787 827388 840945 312060 964804 450194 129745 221629 033750 109684 605526 978283 852482 417382 137618 > 8¹²⁶ [i]