MinT - Best Known (74−25, 74, s)-Nets in Base 2

Best Known (74−25, 74, s)-Nets in Base 2

(74−25, 74, 56)-Net over F₂ — Constructive and digital

Digital (49, 74, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 37, 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]

(74−25, 74, 63)-Net over F₂ — Digital

Digital (49, 74, 63)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−25, 74, 341)-Net in Base 2 — Upper bound on s

There is no (49, 74, 342)-net in base 2, because

1 times m-reduction [i] would yield (49, 73, 342)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 9607 718827 897329 182802 > 2⁷³ [i]