MinT - Best Known (48, 48+45, s)-Nets in Base 2

Best Known (48, 48+45, s)-Nets in Base 2

(48, 48+45, 35)-Net over F₂ — Constructive and digital

Digital (48, 93, 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]

(48, 48+45, 36)-Net over F₂ — Digital

Digital (48, 93, 36)-net over F₂, using

t-expansion [i] based on digital (47, 93, 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]

(48, 48+45, 113)-Net in Base 2 — Upper bound on s

There is no (48, 93, 114)-net in base 2, because

1 times m-reduction [i] would yield (48, 92, 114)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2⁹², 114, S₂, 44), but
  - the linear programming bound shows that MÂ â‰¥ 26 699890 767307 081769 024311 263232 / 4557 > 2⁹² [i]