MinT - Best Known (138−50, 138, s)-Nets in Base 8

Best Known (138−50, 138, s)-Nets in Base 8

(138−50, 138, 354)-Net over F₈ — Constructive and digital

Digital (88, 138, 354)-net over F₈, using

24 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]

(138−50, 138, 576)-Net in Base 8 — Constructive

(88, 138, 576)-net in base 8, using

trace code for nets [i] based on (19, 69, 288)-net in base 64, using
- 1 times m-reduction [i] based on (19, 70, 288)-net in base 64, using
  - base change [i] based on digital (9, 60, 288)-net over F₁₂₈, using
    - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(138−50, 138, 979)-Net over F₈ — Digital

Digital (88, 138, 979)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−50, 138, 140454)-Net in Base 8 — Upper bound on s

There is no (88, 138, 140455)-net in base 8, because

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]