MinT - Best Known (157−66, 157, s)-Nets in Base 8

Best Known (157−66, 157, s)-Nets in Base 8

(157−66, 157, 354)-Net over F₈ — Constructive and digital

Digital (91, 157, 354)-net over F₈, using

11 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]

(157−66, 157, 528)-Net over F₈ — Digital

Digital (91, 157, 528)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−66, 157, 37199)-Net in Base 8 — Upper bound on s

There is no (91, 157, 37200)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6101 596431 631083 655622 749980 683209 956767 397969 433975 445973 041263 323384 939005 435309 178440 108768 018240 107202 860230 928571 910252 515115 022219 306742 > 8¹⁵⁷ [i]