MinT - Best Known (122−78, 122, s)-Nets in Base 2

Best Known (122−78, 122, s)-Nets in Base 2

(122−78, 122, 33)-Net over F₂ — Constructive and digital

Digital (44, 122, 33)-net over F₂, using

t-expansion [i] based on digital (39, 122, 33)-net over F₂, using
- net from sequence [i] based on digital (39, 32)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(122−78, 122, 34)-Net over F₂ — Digital

Digital (44, 122, 34)-net over F₂, using

t-expansion [i] based on digital (43, 122, 34)-net over F₂, using
- net from sequence [i] based on digital (43, 33)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 43 and N(F) ≥ 34, using
    - a curve from the manYPoints database [i]

(122−78, 122, 85)-Net in Base 2 — Upper bound on s

There is no (44, 122, 86)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 394575 498588 828659 646377 670383 750440 > 2¹²² [i]