MinT - Best Known (74, 74+54, s)-Nets in Base 2

Best Known (74, 74+54, s)-Nets in Base 2

(74, 74+54, 54)-Net over F₂ — Constructive and digital

Digital (74, 128, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 64, 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]

(74, 74+54, 57)-Net over F₂ — Digital

Digital (74, 128, 57)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+54, 254)-Net in Base 2 — Upper bound on s

There is no (74, 128, 255)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 359 397167 305450 321603 052202 838698 887942 > 2¹²⁸ [i]