MinT - Best Known (103−69, 103, s)-Nets in Base 8

Best Known (103−69, 103, s)-Nets in Base 8

(103−69, 103, 65)-Net over F₈ — Constructive and digital

Digital (34, 103, 65)-net over F₈, using

t-expansion [i] based on digital (14, 103, 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]

(103−69, 103, 98)-Net over F₈ — Digital

Digital (34, 103, 98)-net over F₈, using

net from sequence [i] based on digital (34, 97)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 34 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(103−69, 103, 968)-Net in Base 8 — Upper bound on s

There is no (34, 103, 969)-net in base 8, because

1 times m-reduction [i] would yield (34, 102, 969)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 131 221840 252404 489094 900995 542031 255764 209990 697642 499447 288343 189805 126003 381039 381376 353048 > 8¹⁰² [i]