MinT - Best Known (105, 168, s)-Nets in Base 8

Best Known (105, 168, s)-Nets in Base 8

(105, 168, 354)-Net over F₈ — Constructive and digital

Digital (105, 168, 354)-net over F₈, using

t-expansion [i] based on digital (93, 168, 354)-net over F₈, using
- 4 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]

(105, 168, 576)-Net in Base 8 — Constructive

(105, 168, 576)-net in base 8, using

trace code for nets [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 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]

(105, 168, 965)-Net over F₈ — Digital

Digital (105, 168, 965)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 168, 129987)-Net in Base 8 — Upper bound on s

There is no (105, 168, 129988)-net in base 8, because

1 times m-reduction [i] would yield (105, 167, 129988)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 546823 015837 336950 701449 562205 176841 685522 617577 729117 363481 475352 488533 530137 330661 337553 381653 135228 964917 391232 998224 411565 323959 931794 690283 915824 > 8¹⁶⁷ [i]