MinT - Best Known (134−55, 134, s)-Nets in Base 2

Best Known (134−55, 134, s)-Nets in Base 2

(134−55, 134, 56)-Net over F₂ — Constructive and digital

Digital (79, 134, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 67, 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]

(134−55, 134, 63)-Net over F₂ — Digital

Digital (79, 134, 63)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−55, 134, 294)-Net in Base 2 — Upper bound on s

There is no (79, 134, 295)-net in base 2, because

1 times m-reduction [i] would yield (79, 133, 295)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11667 363438 980950 719226 599564 640294 688568 > 2¹³³ [i]