MinT - Best Known (163−137, 163, s)-Nets in Base 8

Best Known (163−137, 163, s)-Nets in Base 8

(163−137, 163, 65)-Net over F₈ — Constructive and digital

Digital (26, 163, 65)-net over F₈, using

t-expansion [i] based on digital (14, 163, 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]

(163−137, 163, 86)-Net over F₈ — Digital

Digital (26, 163, 86)-net over F₈, using

t-expansion [i] based on digital (25, 163, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(163−137, 163, 484)-Net in Base 8 — Upper bound on s

There is no (26, 163, 485)-net in base 8, because

13 times m-reduction [i] would yield (26, 150, 485)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2954 148216 718685 416735 644241 256412 783238 023580 258894 240012 823558 102570 212059 174048 081606 966219 721886 096105 577414 716791 575450 240152 993696 > 8¹⁵⁰ [i]