MinT - Best Known (34, 77, s)-Nets in Base 8

Best Known (34, 77, s)-Nets in Base 8

(34, 77, 70)-Net over F₈ — Constructive and digital

Digital (34, 77, 70)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (4, 25, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]
2. digital (9, 52, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(34, 77, 98)-Net over F₈ — Digital

Digital (34, 77, 98)-net over F₈, using

net from sequence [i] based on digital (34, 97)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 34 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(34, 77, 2286)-Net in Base 8 — Upper bound on s

There is no (34, 77, 2287)-net in base 8, because

1 times m-reduction [i] would yield (34, 76, 2287)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 431 428642 515347 963135 451632 252759 317577 032800 844576 247493 340738 481540 > 8⁷⁶ [i]