MinT - Best Known (49, 49+73, s)-Nets in Base 2

Best Known (49, 49+73, s)-Nets in Base 2

(49, 49+73, 35)-Net over F₂ — Constructive and digital

Digital (49, 122, 35)-net over F₂, using

t-expansion [i] based on digital (48, 122, 35)-net over F₂, using
- net from sequence [i] based on digital (48, 34)-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 2 places 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]

(49, 49+73, 36)-Net over F₂ — Digital

Digital (49, 122, 36)-net over F₂, using

t-expansion [i] based on digital (47, 122, 36)-net over F₂, using
- net from sequence [i] based on digital (47, 35)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 47 and N(F) ≥ 36, using
    - Drinfeld modules of rank 1 [i]

(49, 49+73, 100)-Net in Base 2 — Upper bound on s

There is no (49, 122, 101)-net in base 2, because

1 times m-reduction [i] would yield (49, 121, 101)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 860690 679389 728167 562621 957817 484543 > 2¹²¹ [i]