MinT - Best Known (61, 61+39, s)-Nets in Base 2

Best Known (61, 61+39, s)-Nets in Base 2

(61, 61+39, 54)-Net over F₂ — Constructive and digital

Digital (61, 100, 54)-net over F₂, using

2 times m-reduction [i] based on digital (61, 102, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 51, 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]

(61, 61+39, 56)-Net over F₂ — Digital

Digital (61, 100, 56)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+39, 266)-Net in Base 2 — Upper bound on s

There is no (61, 100, 267)-net in base 2, because

1 times m-reduction [i] would yield (61, 99, 267)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 644472 876597 704605 873909 080544 > 2⁹⁹ [i]