MinT - Best Known (144−38, 144, s)-Nets in Base 8

Best Known (144−38, 144, s)-Nets in Base 8

(144−38, 144, 1026)-Net over F₈ — Constructive and digital

Digital (106, 144, 1026)-net over F₈, using

12 times m-reduction [i] based on digital (106, 156, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 78, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(144−38, 144, 6866)-Net over F₈ — Digital

Digital (106, 144, 6866)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−38, 144, 7917504)-Net in Base 8 — Upper bound on s

There is no (106, 144, 7917505)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11090 699221 802972 253273 023698 520958 504153 981863 950887 453383 465130 160630 298315 533035 255952 536396 624862 851188 971540 055847 951203 701952 > 8¹⁴⁴ [i]