MinT - Best Known (117−55, 117, s)-Nets in Base 8

Best Known (117−55, 117, s)-Nets in Base 8

(117−55, 117, 208)-Net over F₈ — Constructive and digital

Digital (62, 117, 208)-net over F₈, using

1 times m-reduction [i] based on digital (62, 118, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 59, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(117−55, 117, 256)-Net over F₈ — Digital

Digital (62, 117, 256)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−55, 117, 11820)-Net in Base 8 — Upper bound on s

There is no (62, 117, 11821)-net in base 8, because

1 times m-reduction [i] would yield (62, 116, 11821)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 574 156805 308853 008151 158291 106747 110570 711316 407158 462501 523064 873759 105230 680756 161979 742730 237283 738568 > 8¹¹⁶ [i]