MinT - Best Known (148−55, 148, s)-Nets in Base 8

Best Known (148−55, 148, s)-Nets in Base 8

(148−55, 148, 354)-Net over F₈ — Constructive and digital

Digital (93, 148, 354)-net over F₈, using

24 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]

(148−55, 148, 514)-Net in Base 8 — Constructive

(93, 148, 514)-net in base 8, using

base change [i] based on digital (56, 111, 514)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (56, 112, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 56, 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]

(148−55, 148, 911)-Net over F₈ — Digital

Digital (93, 148, 911)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−55, 148, 128847)-Net in Base 8 — Upper bound on s

There is no (93, 148, 128848)-net in base 8, because

1 times m-reduction [i] would yield (93, 147, 128848)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 679310 809991 390026 109146 135844 137377 705236 841868 638080 197697 864320 763798 667858 588212 519889 801642 710941 400540 047337 923497 021196 009388 > 8¹⁴⁷ [i]