MinT - Best Known (150−57, 150, s)-Nets in Base 8

Best Known (150−57, 150, s)-Nets in Base 8

(150−57, 150, 354)-Net over F₈ — Constructive and digital

Digital (93, 150, 354)-net over F₈, using

22 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]

(150−57, 150, 432)-Net in Base 8 — Constructive

(93, 150, 432)-net in base 8, using

4 times m-reduction [i] based on (93, 154, 432)-net in base 8, using
- trace code for nets [i] based on (16, 77, 216)-net in base 64, using
  - base change [i] based on digital (5, 66, 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]

(150−57, 150, 822)-Net over F₈ — Digital

Digital (93, 150, 822)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−57, 150, 103172)-Net in Base 8 — Upper bound on s

There is no (93, 150, 103173)-net in base 8, because

1 times m-reduction [i] would yield (93, 149, 103173)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 363 509914 573985 210794 308390 765225 762497 080926 484970 662832 167573 591334 143527 544360 625542 447421 913639 656225 410858 138103 254172 250169 524640 > 8¹⁴⁹ [i]