MinT - Best Known (257−55, 257, s)-Nets in Base 2

Best Known (257−55, 257, s)-Nets in Base 2

(257−55, 257, 260)-Net over F₂ — Constructive and digital

Digital (202, 257, 260)-net over F₂, using

t-expansion [i] based on digital (201, 257, 260)-net over F₂, using
- 3 times m-reduction [i] based on digital (201, 260, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 65, 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]

(257−55, 257, 525)-Net over F₂ — Digital

Digital (202, 257, 525)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−55, 257, 7769)-Net in Base 2 — Upper bound on s

There is no (202, 257, 7770)-net in base 2, because

1 times m-reduction [i] would yield (202, 256, 7770)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 115999 139213 931285 366599 579925 428070 493021 517299 643253 602567 587015 816845 603412 > 2²⁵⁶ [i]