MinT - Best Known (133−63, 133, s)-Nets in Base 8

Best Known (133−63, 133, s)-Nets in Base 8

(133−63, 133, 208)-Net over F₈ — Constructive and digital

Digital (70, 133, 208)-net over F₈, using

1 times m-reduction [i] based on digital (70, 134, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 67, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(133−63, 133, 276)-Net over F₈ — Digital

Digital (70, 133, 276)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−63, 133, 12407)-Net in Base 8 — Upper bound on s

There is no (70, 133, 12408)-net in base 8, because

1 times m-reduction [i] would yield (70, 132, 12408)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 161743 530381 753798 565990 825543 697207 960986 516873 042682 490450 176997 321208 095049 889417 401443 075424 412607 613885 070948 818740 > 8¹³² [i]