MinT - Best Known (128−52, 128, s)-Nets in Base 2

Best Known (128−52, 128, s)-Nets in Base 2

(128−52, 128, 56)-Net over F₂ — Constructive and digital

Digital (76, 128, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 64, 28)-net over F₄, using
- net from sequence [i] based on digital (12, 27)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(128−52, 128, 62)-Net over F₂ — Digital

Digital (76, 128, 62)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−52, 128, 283)-Net in Base 2 — Upper bound on s

There is no (76, 128, 284)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 352 065077 869461 798525 886556 954032 992155 > 2¹²⁸ [i]