MinT - Best Known (95, 95+59, s)-Nets in Base 8

Best Known (95, 95+59, s)-Nets in Base 8

(95, 95+59, 354)-Net over F₈ — Constructive and digital

Digital (95, 154, 354)-net over F₈, using

t-expansion [i] based on digital (93, 154, 354)-net over F₈, using
- 18 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(95, 95+59, 432)-Net in Base 8 — Constructive

(95, 154, 432)-net in base 8, using

t-expansion [i] based on (93, 154, 432)-net in base 8, using
- trace code for nets [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]

(95, 95+59, 806)-Net over F₈ — Digital

Digital (95, 154, 806)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(95, 95+59, 96943)-Net in Base 8 — Upper bound on s

There is no (95, 154, 96944)-net in base 8, because

1 times m-reduction [i] would yield (95, 153, 96944)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 488566 167380 766667 343885 668375 584416 843302 483688 518812 840019 193007 007516 970837 275071 527554 535634 510860 214531 794875 885694 177412 768672 897406 > 8¹⁵³ [i]