MinT - Best Known (161, 161+37, s)-Nets in Base 2

Best Known (161, 161+37, s)-Nets in Base 2

(161, 161+37, 271)-Net over F₂ — Constructive and digital

Digital (161, 198, 271)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (8, 26, 11)-net over F₂, using
  - net from sequence [i] based on digital (8, 10)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 8 and N(F) ≥ 11, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (135, 172, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 43, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(161, 161+37, 644)-Net over F₂ — Digital

Digital (161, 198, 644)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+37, 14858)-Net in Base 2 — Upper bound on s

There is no (161, 198, 14859)-net in base 2, because

1 times m-reduction [i] would yield (161, 197, 14859)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 201089 506329 279304 078006 862157 050556 718941 290147 061803 790880 > 2¹⁹⁷ [i]