MinT - Best Known (189, 189+51, s)-Nets in Base 2

Best Known (189, 189+51, s)-Nets in Base 2

(189, 189+51, 260)-Net over F₂ — Constructive and digital

Digital (189, 240, 260)-net over F₂, using

4 times m-reduction [i] based on digital (189, 244, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 61, 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]

(189, 189+51, 505)-Net over F₂ — Digital

Digital (189, 240, 505)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(189, 189+51, 7645)-Net in Base 2 — Upper bound on s

There is no (189, 240, 7646)-net in base 2, because

1 times m-reduction [i] would yield (189, 239, 7646)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 886156 311460 993199 830068 042351 264566 664141 287787 831999 067204 119431 114457 > 2²³⁹ [i]