MinT - Best Known (252−55, 252, s)-Nets in Base 2

Best Known (252−55, 252, s)-Nets in Base 2

(252−55, 252, 260)-Net over F₂ — Constructive and digital

Digital (197, 252, 260)-net over F₂, using

t-expansion [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]

(252−55, 252, 488)-Net over F₂ — Digital

Digital (197, 252, 488)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−55, 252, 6828)-Net in Base 2 — Upper bound on s

There is no (197, 252, 6829)-net in base 2, because

1 times m-reduction [i] would yield (197, 251, 6829)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3622 102857 782571 195617 762752 966620 244072 341949 441280 057212 315593 782932 685120 > 2²⁵¹ [i]