MinT - Best Known (36, 78, s)-Nets in Base 8

Best Known (36, 78, s)-Nets in Base 8

(36, 78, 79)-Net over F₈ — Constructive and digital

Digital (36, 78, 79)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 22, 14)-net over F₈, using
  - net from sequence [i] based on digital (1, 13)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
2. digital (14, 56, 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, 78, 112)-Net over F₈ — Digital

Digital (36, 78, 112)-net over F₈, using

t-expansion [i] based on digital (35, 78, 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, 78, 2790)-Net in Base 8 — Upper bound on s

There is no (36, 78, 2791)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 27668 919617 489750 885396 696516 709623 253932 000462 694210 450510 377886 296164 > 8⁷⁸ [i]