MinT - Best Known (78, 78+58, s)-Nets in Base 2

Best Known (78, 78+58, s)-Nets in Base 2

(78, 78+58, 54)-Net over F₂ — Constructive and digital

Digital (78, 136, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 68, 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]

(78, 78+58, 58)-Net over F₂ — Digital

Digital (78, 136, 58)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+58, 260)-Net in Base 2 — Upper bound on s

There is no (78, 136, 261)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 88854 900126 646759 294551 332767 979012 668352 > 2¹³⁶ [i]