MinT - Best Known (80−34, 80, s)-Nets in Base 2

Best Known (80−34, 80, s)-Nets in Base 2

(80−34, 80, 34)-Net over F₂ — Constructive and digital

Digital (46, 80, 34)-net over F₂, using

t-expansion [i] based on digital (45, 80, 34)-net over F₂, using
- net from sequence [i] based on digital (45, 33)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 41, N(F)Â =Â 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F₂ with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]

(80−34, 80, 40)-Net over F₂ — Digital

Digital (46, 80, 40)-net over F₂, using

trace code for nets [i] based on digital (6, 40, 20)-net over F₄, using
- net from sequence [i] based on digital (6, 19)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 6 and N(F) ≥ 20, using
    - Drinfeld modules of rank 1 [i]

(80−34, 80, 163)-Net in Base 2 — Upper bound on s

There is no (46, 80, 164)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 240124 948454 811333 391782 > 2⁸⁰ [i]