MinT - Best Known (251−51, 251, s)-Nets in Base 2

Best Known (251−51, 251, s)-Nets in Base 2

(251−51, 251, 260)-Net over F₂ — Constructive and digital

Digital (200, 251, 260)-net over F₂, using

t-expansion [i] based on digital (198, 251, 260)-net over F₂, using
- 5 times m-reduction [i] based on digital (198, 256, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 64, 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]

(251−51, 251, 598)-Net over F₂ — Digital

Digital (200, 251, 598)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−51, 251, 10384)-Net in Base 2 — Upper bound on s

There is no (200, 251, 10385)-net in base 2, because

1 times m-reduction [i] would yield (200, 250, 10385)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1811 626225 143318 403442 382384 252449 764104 458424 864674 146289 168290 746735 464352 > 2²⁵⁰ [i]