MinT - Best Known (141−105, 141, s)-Nets in Base 8

Best Known (141−105, 141, s)-Nets in Base 8

(141−105, 141, 65)-Net over F₈ — Constructive and digital

Digital (36, 141, 65)-net over F₈, using

t-expansion [i] based on digital (14, 141, 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]

(141−105, 141, 112)-Net over F₈ — Digital

Digital (36, 141, 112)-net over F₈, using

t-expansion [i] based on digital (35, 141, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(141−105, 141, 747)-Net in Base 8 — Upper bound on s

There is no (36, 141, 748)-net in base 8, because

1 times m-reduction [i] would yield (36, 140, 748)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 768554 315571 084863 980974 251821 812539 214501 409594 403250 622802 219096 728755 791457 053963 825640 366278 563411 967060 408608 451557 746632 > 8¹⁴⁰ [i]