MinT - Best Known (156−68, 156, s)-Nets in Base 8

Best Known (156−68, 156, s)-Nets in Base 8

(156−68, 156, 354)-Net over F₈ — Constructive and digital

Digital (88, 156, 354)-net over F₈, using

6 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]

(156−68, 156, 450)-Net over F₈ — Digital

Digital (88, 156, 450)-net over F₈, using

trace code for nets [i] based on digital (10, 78, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(156−68, 156, 26891)-Net in Base 8 — Upper bound on s

There is no (88, 156, 26892)-net in base 8, because

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]