MinT - Best Known (52, 52+32, s)-Nets in Base 2

Best Known (52, 52+32, s)-Nets in Base 2

(52, 52+32, 54)-Net over F₂ — Constructive and digital

Digital (52, 84, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 42, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(52, 52+32, 236)-Net in Base 2 — Upper bound on s

There is no (52, 84, 237)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20 311099 992029 217159 750214 > 2⁸⁴ [i]