MinT - Best Known (79, 79+49, s)-Nets in Base 8

Best Known (79, 79+49, s)-Nets in Base 8

(79, 79+49, 354)-Net over F₈ — Constructive and digital

Digital (79, 128, 354)-net over F₈, using

16 times m-reduction [i] based on digital (79, 144, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 72, 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]

(79, 79+49, 432)-Net in Base 8 — Constructive

(79, 128, 432)-net in base 8, using

8² times duplication [i] based on (77, 126, 432)-net in base 8, using
- trace code for nets [i] based on (14, 63, 216)-net in base 64, using
  - base change [i] based on digital (5, 54, 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]

(79, 79+49, 698)-Net over F₈ — Digital

Digital (79, 128, 698)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+49, 84147)-Net in Base 8 — Upper bound on s

There is no (79, 128, 84148)-net in base 8, because

1 times m-reduction [i] would yield (79, 127, 84148)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 926600 245484 009013 963676 261481 965088 987866 728326 079355 753173 117121 520162 870907 662194 216930 481245 508636 812398 446524 > 8¹²⁷ [i]