MinT - Best Known (61, 61+31, s)-Nets in Base 2

Best Known (61, 61+31, s)-Nets in Base 2

(61, 61+31, 66)-Net over F₂ — Constructive and digital

Digital (61, 92, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 46, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(61, 61+31, 74)-Net over F₂ — Digital

Digital (61, 92, 74)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+31, 409)-Net in Base 2 — Upper bound on s

There is no (61, 92, 410)-net in base 2, because

1 times m-reduction [i] would yield (61, 91, 410)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2560 345063 831274 492129 413240 > 2⁹¹ [i]