MinT - Best Known (50, 105, s)-Nets in Base 8

Best Known (50, 105, s)-Nets in Base 8

(50, 105, 110)-Net over F₈ — Constructive and digital

Digital (50, 105, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 36, 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]
2. digital (14, 69, 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]

(50, 105, 150)-Net over F₈ — Digital

Digital (50, 105, 150)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 105, 4680)-Net in Base 8 — Upper bound on s

There is no (50, 105, 4681)-net in base 8, because

1 times m-reduction [i] would yield (50, 104, 4681)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8354 347993 475064 180568 362622 590043 276220 548664 679667 584688 367165 995546 421629 203110 711299 469248 > 8¹⁰⁴ [i]