MinT - Best Known (162−71, 162, s)-Nets in Base 8

Best Known (162−71, 162, s)-Nets in Base 8

(162−71, 162, 354)-Net over F₈ — Constructive and digital

Digital (91, 162, 354)-net over F₈, using

6 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]

(162−71, 162, 452)-Net over F₈ — Digital

Digital (91, 162, 452)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−71, 162, 28316)-Net in Base 8 — Upper bound on s

There is no (91, 162, 28317)-net in base 8, because

1 times m-reduction [i] would yield (91, 161, 28317)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 24 983552 446620 787367 240580 224667 749157 493228 225103 352535 374047 936913 940675 177431 988662 691781 627982 590206 866115 939073 910740 313669 075964 614442 359504 > 8¹⁶¹ [i]