MinT - Best Known (76, 119, s)-Nets in Base 8

Best Known (76, 119, s)-Nets in Base 8

(76, 119, 354)-Net over F₈ — Constructive and digital

Digital (76, 119, 354)-net over F₈, using

19 times m-reduction [i] based on digital (76, 138, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 69, 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]

(76, 119, 516)-Net in Base 8 — Constructive

(76, 119, 516)-net in base 8, using

1 times m-reduction [i] based on (76, 120, 516)-net in base 8, using
- base change [i] based on digital (46, 90, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 45, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(76, 119, 875)-Net over F₈ — Digital

Digital (76, 119, 875)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 119, 147184)-Net in Base 8 — Upper bound on s

There is no (76, 119, 147185)-net in base 8, because

1 times m-reduction [i] would yield (76, 118, 147185)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 36699 065044 265736 140137 363729 700210 315849 727915 705935 120921 604389 504380 671778 274366 677893 793399 872437 173792 > 8¹¹⁸ [i]