MinT - Best Known (88, 88+55, s)-Nets in Base 8

Best Known (88, 88+55, s)-Nets in Base 8

(88, 88+55, 354)-Net over F₈ — Constructive and digital

Digital (88, 143, 354)-net over F₈, using

19 times m-reduction [i] based on digital (88, 162, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 81, 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]

(88, 88+55, 432)-Net in Base 8 — Constructive

(88, 143, 432)-net in base 8, using

1 times m-reduction [i] based on (88, 144, 432)-net in base 8, using
- trace code for nets [i] based on (16, 72, 216)-net in base 64, using
  - 5 times m-reduction [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]

(88, 88+55, 744)-Net over F₈ — Digital

Digital (88, 143, 744)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+55, 87661)-Net in Base 8 — Upper bound on s

There is no (88, 143, 87662)-net in base 8, because

1 times m-reduction [i] would yield (88, 142, 87662)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 310918 808938 569983 363103 866310 351235 129163 699068 271369 056866 613366 981427 367961 984622 650809 018305 103168 554269 356235 141854 686700 > 8¹⁴² [i]