MinT - Best Known (141−86, 141, s)-Nets in Base 2

Best Known (141−86, 141, s)-Nets in Base 2

(141−86, 141, 42)-Net over F₂ — Constructive and digital

Digital (55, 141, 42)-net over F₂, using

t-expansion [i] based on digital (54, 141, 42)-net over F₂, using
- net from sequence [i] based on digital (54, 41)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(141−86, 141, 109)-Net in Base 2 — Upper bound on s

There is no (55, 141, 110)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 306374 811469 989684 124603 977571 376689 540530 > 2¹⁴¹ [i]