MinT - Best Known (90, 143, s)-Nets in Base 8

Best Known (90, 143, s)-Nets in Base 8

(90, 143, 354)-Net over F₈ — Constructive and digital

Digital (90, 143, 354)-net over F₈, using

23 times m-reduction [i] based on digital (90, 166, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 83, 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]

(90, 143, 514)-Net in Base 8 — Constructive

(90, 143, 514)-net in base 8, using

1 times m-reduction [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]

(90, 143, 899)-Net over F₈ — Digital

Digital (90, 143, 899)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 143, 128943)-Net in Base 8 — Upper bound on s

There is no (90, 143, 128944)-net in base 8, because

1 times m-reduction [i] would yield (90, 142, 128944)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 292336 415094 677564 423521 892945 792076 284247 297487 561963 157844 894359 471402 199176 949716 013670 859065 457094 359130 477052 320099 089318 > 8¹⁴² [i]