MinT - Best Known (150−59, 150, s)-Nets in Base 8

Best Known (150−59, 150, s)-Nets in Base 8

(150−59, 150, 354)-Net over F₈ — Constructive and digital

Digital (91, 150, 354)-net over F₈, using

18 times m-reduction [i] based on digital (91, 168, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 84, 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]

(150−59, 150, 432)-Net in Base 8 — Constructive

(91, 150, 432)-net in base 8, using

trace code for nets [i] based on (16, 75, 216)-net in base 64, using
- 2 times m-reduction [i] based on (16, 77, 216)-net in base 64, using
  - base change [i] based on digital (5, 66, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(150−59, 150, 693)-Net over F₈ — Digital

Digital (91, 150, 693)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−59, 150, 72766)-Net in Base 8 — Upper bound on s

There is no (91, 150, 72767)-net in base 8, because

1 times m-reduction [i] would yield (91, 149, 72767)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 363 532734 239029 135562 134938 684805 624749 662065 233512 004590 041900 542249 662451 261319 521154 497129 193488 685131 946722 640882 698964 596945 102366 > 8¹⁴⁹ [i]