MinT - Best Known (258−55, 258, s)-Nets in Base 2

Best Known (258−55, 258, s)-Nets in Base 2

(258−55, 258, 260)-Net over F₂ — Constructive and digital

Digital (203, 258, 260)-net over F₂, using

t-expansion [i] based on digital (201, 258, 260)-net over F₂, using
- 2 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]

(258−55, 258, 532)-Net over F₂ — Digital

Digital (203, 258, 532)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−55, 258, 7972)-Net in Base 2 — Upper bound on s

There is no (203, 258, 7973)-net in base 2, because

1 times m-reduction [i] would yield (203, 257, 7973)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 231927 751255 210228 221142 451330 283926 128634 092059 995535 610545 690405 639674 511360 > 2²⁵⁷ [i]