MinT - Best Known (193−43, 193, s)-Nets in Base 2

Best Known (193−43, 193, s)-Nets in Base 2

(193−43, 193, 200)-Net over F₂ — Constructive and digital

Digital (150, 193, 200)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (1, 22, 5)-net over F₂, using
  - net from sequence [i] based on digital (1, 4)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (128, 171, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 57, 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]

(193−43, 193, 368)-Net over F₂ — Digital

Digital (150, 193, 368)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−43, 193, 4875)-Net in Base 2 — Upper bound on s

There is no (150, 193, 4876)-net in base 2, because

1 times m-reduction [i] would yield (150, 192, 4876)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6289 670402 761039 251775 700689 843808 067446 770654 586321 867552 > 2¹⁹² [i]