MinT - Best Known (190, 190+57, s)-Nets in Base 2

Best Known (190, 190+57, s)-Nets in Base 2

(190, 190+57, 205)-Net over F₂ — Constructive and digital

Digital (190, 247, 205)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 34, 10)-net over F₂, using
  - net from sequence [i] based on digital (6, 9)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
      - an explicitly constructive algebraic function field [i]
2. digital (156, 213, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 71, 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]

(190, 190+57, 414)-Net over F₂ — Digital

Digital (190, 247, 414)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(190, 190+57, 4944)-Net in Base 2 — Upper bound on s

There is no (190, 247, 4945)-net in base 2, because

1 times m-reduction [i] would yield (190, 246, 4945)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 113 177071 218082 116697 095737 784968 610283 443735 764217 384350 820608 529899 573104 > 2²⁴⁶ [i]