MinT - Best Known (250−54, 250, s)-Nets in Base 2

Best Known (250−54, 250, s)-Nets in Base 2

(250−54, 250, 260)-Net over F₂ — Constructive and digital

Digital (196, 250, 260)-net over F₂, using

t-expansion [i] based on digital (195, 250, 260)-net over F₂, using
- 2 times m-reduction [i] based on digital (195, 252, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 63, 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]

(250−54, 250, 499)-Net over F₂ — Digital

Digital (196, 250, 499)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−54, 250, 6654)-Net in Base 2 — Upper bound on s

There is no (196, 250, 6655)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1811 723843 698342 944215 022106 035678 356236 717468 544543 824895 415652 308236 386598 > 2²⁵⁰ [i]