MinT - Best Known (163−70, 163, s)-Nets in Base 8

Best Known (163−70, 163, s)-Nets in Base 8

(163−70, 163, 354)-Net over F₈ — Constructive and digital

Digital (93, 163, 354)-net over F₈, using

9 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]

(163−70, 163, 496)-Net over F₈ — Digital

Digital (93, 163, 496)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−70, 163, 31892)-Net in Base 8 — Upper bound on s

There is no (93, 163, 31893)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1599 617876 081790 928169 756143 008772 296099 877564 177217 461095 000930 274332 403485 042343 434625 765923 641630 837314 242691 704116 061405 542373 435587 461016 763056 > 8¹⁶³ [i]