MinT - Best Known (52, 52+38, s)-Nets in Base 2

Best Known (52, 52+38, s)-Nets in Base 2

(52, 52+38, 42)-Net over F₂ — Constructive and digital

Digital (52, 90, 42)-net over F₂, using

trace code for nets [i] based on digital (7, 45, 21)-net over F₄, using
- net from sequence [i] based on digital (7, 20)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(52, 52+38, 44)-Net over F₂ — Digital

Digital (52, 90, 44)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+38, 184)-Net in Base 2 — Upper bound on s

There is no (52, 90, 185)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1238 676809 827549 731232 838280 > 2⁹⁰ [i]