MinT - Best Known (157−69, 157, s)-Nets in Base 8

Best Known (157−69, 157, s)-Nets in Base 8

(157−69, 157, 354)-Net over F₈ — Constructive and digital

Digital (88, 157, 354)-net over F₈, using

5 times m-reduction [i] based on digital (88, 162, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 81, 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]

(157−69, 157, 435)-Net over F₈ — Digital

Digital (88, 157, 435)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−69, 157, 26891)-Net in Base 8 — Upper bound on s

There is no (88, 157, 26892)-net in base 8, because

1 times m-reduction [i] would yield (88, 156, 26892)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 762 208248 544284 624961 064552 038085 090730 159757 964456 292590 477453 824518 437229 274015 106791 260119 114858 509591 626914 983898 455885 578518 532534 421864 > 8¹⁵⁶ [i]