MinT - Best Known (121−61, 121, s)-Nets in Base 8

Best Known (121−61, 121, s)-Nets in Base 8

(121−61, 121, 130)-Net over F₈ — Constructive and digital

Digital (60, 121, 130)-net over F₈, using

3 times m-reduction [i] based on digital (60, 124, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 46, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]
  2. digital (14, 78, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(121−61, 121, 197)-Net over F₈ — Digital

Digital (60, 121, 197)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−61, 121, 7028)-Net in Base 8 — Upper bound on s

There is no (60, 121, 7029)-net in base 8, because

1 times m-reduction [i] would yield (60, 120, 7029)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 348731 830492 612989 581073 221633 765358 495716 212637 173244 318437 618919 167535 260239 227573 247872 638463 841986 458640 > 8¹²⁰ [i]