MinT - Best Known (82, 82+63, s)-Nets in Base 8

Best Known (82, 82+63, s)-Nets in Base 8

(82, 82+63, 354)-Net over F₈ — Constructive and digital

Digital (82, 145, 354)-net over F₈, using

5 times m-reduction [i] based on digital (82, 150, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 75, 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]

(82, 82+63, 427)-Net over F₈ — Digital

Digital (82, 145, 427)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+63, 27773)-Net in Base 8 — Upper bound on s

There is no (82, 145, 27774)-net in base 8, because

1 times m-reduction [i] would yield (82, 144, 27774)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11097 401618 010791 803858 633044 408550 405977 664471 699254 807139 037594 164555 906950 154329 144992 936154 162890 950585 387129 867249 857267 202192 > 8¹⁴⁴ [i]