MinT - Best Known (107−72, 107, s)-Nets in Base 8

Best Known (107−72, 107, s)-Nets in Base 8

(107−72, 107, 65)-Net over F₈ — Constructive and digital

Digital (35, 107, 65)-net over F₈, using

t-expansion [i] based on digital (14, 107, 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]

(107−72, 107, 112)-Net over F₈ — Digital

Digital (35, 107, 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]

(107−72, 107, 963)-Net in Base 8 — Upper bound on s

There is no (35, 107, 964)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 367753 995331 173928 837983 490421 298156 584800 919895 858947 600003 623161 459679 413020 876428 132076 403792 > 8¹⁰⁷ [i]