MinT - Best Known (135−110, 135, s)-Nets in Base 8

Best Known (135−110, 135, s)-Nets in Base 8

(135−110, 135, 65)-Net over F₈ — Constructive and digital

Digital (25, 135, 65)-net over F₈, using

t-expansion [i] based on digital (14, 135, 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]

(135−110, 135, 86)-Net over F₈ — Digital

Digital (25, 135, 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]

(135−110, 135, 467)-Net in Base 8 — Upper bound on s

There is no (25, 135, 468)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 83 611231 743679 100494 239878 597248 056097 413929 885040 766678 160485 048805 010629 833575 095412 382570 555369 722080 045985 980648 213968 > 8¹³⁵ [i]