MinT - Best Known (173−66, 173, s)-Nets in Base 8

Best Known (173−66, 173, s)-Nets in Base 8

(173−66, 173, 354)-Net over F₈ — Constructive and digital

Digital (107, 173, 354)-net over F₈, using

8¹ times duplication [i] based on digital (106, 172, 354)-net over F₈, using
- t-expansion [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]

(173−66, 173, 432)-Net in Base 8 — Constructive

(107, 173, 432)-net in base 8, using

8¹ times duplication [i] based on (106, 172, 432)-net in base 8, using
- t-expansion [i] based on (104, 172, 432)-net in base 8, using
  - trace code for nets [i] based on (18, 86, 216)-net in base 64, using
    - 5 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
      - base change [i] based on digital (5, 78, 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]

(173−66, 173, 907)-Net over F₈ — Digital

Digital (107, 173, 907)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−66, 173, 101987)-Net in Base 8 — Upper bound on s

There is no (107, 173, 101988)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 716245 797007 764753 103430 125726 265536 760007 194770 272973 123718 405227 307130 432791 688425 703099 679594 212432 048522 708206 453714 783705 201941 359401 104886 183399 631667 > 8¹⁷³ [i]