MinT - Best Known (88, 88+52, s)-Nets in Base 8

Best Known (88, 88+52, s)-Nets in Base 8

(88, 88+52, 354)-Net over F₈ — Constructive and digital

Digital (88, 140, 354)-net over F₈, using

22 times m-reduction [i] based on digital (88, 162, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 81, 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]

(88, 88+52, 514)-Net in Base 8 — Constructive

(88, 140, 514)-net in base 8, using

base change [i] based on digital (53, 105, 514)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (53, 106, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 53, 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]

(88, 88+52, 874)-Net over F₈ — Digital

Digital (88, 140, 874)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+52, 109881)-Net in Base 8 — Upper bound on s

There is no (88, 140, 109882)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 708235 747477 503724 343311 674258 936175 175161 346875 020745 428688 674046 419276 801368 067420 185400 485969 810816 115444 758743 202789 134400 > 8¹⁴⁰ [i]