MinT - Best Known (146−54, 146, s)-Nets in Base 8

Best Known (146−54, 146, s)-Nets in Base 8

(146−54, 146, 354)-Net over F₈ — Constructive and digital

Digital (92, 146, 354)-net over F₈, using

24 times m-reduction [i] based on digital (92, 170, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 85, 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]

(146−54, 146, 514)-Net in Base 8 — Constructive

(92, 146, 514)-net in base 8, using

8² times duplication [i] based on (90, 144, 514)-net in base 8, using
- base change [i] based on digital (54, 108, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 54, 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]

(146−54, 146, 924)-Net over F₈ — Digital

Digital (92, 146, 924)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−54, 146, 119295)-Net in Base 8 — Upper bound on s

There is no (92, 146, 119296)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 709937 066756 602211 687299 146768 988927 400044 638755 572969 062912 861865 734245 690560 907716 589244 020366 792399 559269 547070 568372 451714 805345 > 8¹⁴⁶ [i]