MinT - Best Known (89, 150, s)-Nets in Base 8

Best Known (89, 150, s)-Nets in Base 8

(89, 150, 354)-Net over F₈ — Constructive and digital

Digital (89, 150, 354)-net over F₈, using

14 times m-reduction [i] based on digital (89, 164, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 82, 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]

(89, 150, 384)-Net in Base 8 — Constructive

(89, 150, 384)-net in base 8, using

trace code for nets [i] based on (14, 75, 192)-net in base 64, using
- 2 times m-reduction [i] based on (14, 77, 192)-net in base 64, using
  - base change [i] based on digital (3, 66, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(89, 150, 592)-Net over F₈ — Digital

Digital (89, 150, 592)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 150, 52587)-Net in Base 8 — Upper bound on s

There is no (89, 150, 52588)-net in base 8, because

1 times m-reduction [i] would yield (89, 149, 52588)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 363 524452 119717 347032 549527 005069 552653 649728 262657 006483 986479 115440 170822 960127 417992 639323 301334 895350 973646 426492 816078 570067 462808 > 8¹⁴⁹ [i]