MinT - Best Known (36, 36+44, s)-Nets in Base 8

Best Known (36, 36+44, s)-Nets in Base 8

(36, 36+44, 74)-Net over F₈ — Constructive and digital

Digital (36, 80, 74)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (0, 22, 9)-net over F₈, using
  - net from sequence [i] based on digital (0, 8)-sequence over F₈, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 0 and N(F) ≥ 9, using
      - the rational function field F₈(x) [i]
    - Niederreiter sequence [i]
2. digital (14, 58, 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]

(36, 36+44, 112)-Net over F₈ — Digital

Digital (36, 80, 112)-net over F₈, using

t-expansion [i] based on digital (35, 80, 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]

(36, 36+44, 2473)-Net in Base 8 — Upper bound on s

There is no (36, 80, 2474)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 772710 638569 717235 798868 314891 693758 956678 766865 044049 384464 740050 072792 > 8⁸⁰ [i]