MinT - Best Known (195−114, 195, s)-Nets in Base 2

Best Known (195−114, 195, s)-Nets in Base 2

(195−114, 195, 51)-Net over F₂ — Constructive and digital

Digital (81, 195, 51)-net over F₂, using

t-expansion [i] based on digital (80, 195, 51)-net over F₂, using
- net from sequence [i] based on digital (80, 50)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, 1 place with degree 2, and 2 places with degree 6 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

(195−114, 195, 56)-Net over F₂ — Digital

Digital (81, 195, 56)-net over F₂, using

t-expansion [i] based on digital (80, 195, 56)-net over F₂, using
- net from sequence [i] based on digital (80, 55)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 80 and N(F) ≥ 56, using
    - Drinfeld modules of rank 1 [i]

(195−114, 195, 163)-Net in Base 2 — Upper bound on s

There is no (81, 195, 164)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 60676 546302 717958 463849 477888 982199 437580 913115 629514 089648 > 2¹⁹⁵ [i]