MinT - Best Known (163−75, 163, s)-Nets in Base 8

Best Known (163−75, 163, s)-Nets in Base 8

(163−75, 163, 256)-Net over F₈ — Constructive and digital

Digital (88, 163, 256)-net over F₈, using

3 times m-reduction [i] based on digital (88, 166, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 83, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(163−75, 163, 371)-Net over F₈ — Digital

Digital (88, 163, 371)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−75, 163, 18808)-Net in Base 8 — Upper bound on s

There is no (88, 163, 18809)-net in base 8, because

1 times m-reduction [i] would yield (88, 162, 18809)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 200 122249 907004 801259 300486 273866 716243 516011 894416 550921 989970 250020 592205 071348 483326 962684 296447 576378 443693 653907 185315 021892 874754 903709 186344 > 8¹⁶² [i]