MinT - Best Known (77, 77+43, s)-Nets in Base 8

Best Known (77, 77+43, s)-Nets in Base 8

(77, 77+43, 354)-Net over F₈ — Constructive and digital

Digital (77, 120, 354)-net over F₈, using

20 times m-reduction [i] based on digital (77, 140, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 70, 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]

(77, 77+43, 518)-Net in Base 8 — Constructive

(77, 120, 518)-net in base 8, using

base change [i] based on digital (47, 90, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 45, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(77, 77+43, 918)-Net over F₈ — Digital

Digital (77, 120, 918)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+43, 162506)-Net in Base 8 — Upper bound on s

There is no (77, 120, 162507)-net in base 8, because

1 times m-reduction [i] would yield (77, 119, 162507)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 293601 315586 364370 526120 327292 490785 012248 428972 953280 413136 552628 484441 327184 148688 755982 013403 175491 738640 > 8¹¹⁹ [i]