MinT - Best Known (88, 139, s)-Nets in Base 8

Best Known (88, 139, s)-Nets in Base 8

(88, 139, 354)-Net over F₈ — Constructive and digital

Digital (88, 139, 354)-net over F₈, using

23 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, 139, 514)-Net in Base 8 — Constructive

(88, 139, 514)-net in base 8, using

1 times m-reduction [i] based on (88, 140, 514)-net in base 8, using
- base change [i] based on digital (53, 105, 514)-net over F₁₆, using
  - 1 times m-reduction [i] based on digital (53, 106, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 53, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]

(88, 139, 927)-Net over F₈ — Digital

Digital (88, 139, 927)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 139, 140454)-Net in Base 8 — Upper bound on s

There is no (88, 139, 140455)-net in base 8, because

1 times m-reduction [i] would yield (88, 138, 140455)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42309 608643 765496 766543 075080 930736 669238 106875 007901 115172 105560 402574 901768 856196 007234 344018 774796 688696 458065 337204 024744 > 8¹³⁸ [i]