MinT - Best Known (170, 219, s)-Nets in Base 2

Best Known (170, 219, s)-Nets in Base 2

(170, 219, 205)-Net over F₂ — Constructive and digital

Digital (170, 219, 205)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 30, 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]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (140, 189, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 63, 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]

(170, 219, 405)-Net over F₂ — Digital

Digital (170, 219, 405)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(170, 219, 5282)-Net in Base 2 — Upper bound on s

There is no (170, 219, 5283)-net in base 2, because

1 times m-reduction [i] would yield (170, 218, 5283)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 422690 857433 565633 689602 585721 110391 738122 610304 828059 117603 555612 > 2²¹⁸ [i]