MinT - Best Known (250−51, 250, s)-Nets in Base 2

Best Known (250−51, 250, s)-Nets in Base 2

(250−51, 250, 260)-Net over F₂ — Constructive and digital

Digital (199, 250, 260)-net over F₂, using

t-expansion [i] based on digital (198, 250, 260)-net over F₂, using
- 6 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]

(250−51, 250, 589)-Net over F₂ — Digital

Digital (199, 250, 589)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−51, 250, 10099)-Net in Base 2 — Upper bound on s

There is no (199, 250, 10100)-net in base 2, because

1 times m-reduction [i] would yield (199, 249, 10100)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 905 783664 104541 207728 493137 812431 600488 063638 069488 783260 058100 656486 579780 > 2²⁴⁹ [i]