MinT - Best Known (139−102, 139, s)-Nets in Base 2

Best Known (139−102, 139, s)-Nets in Base 2

(139−102, 139, 24)-Net over F₂ — Constructive and digital

Digital (37, 139, 24)-net over F₂, using

t-expansion [i] based on digital (33, 139, 24)-net over F₂, using
- net from sequence [i] based on digital (33, 23)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(139−102, 139, 30)-Net over F₂ — Digital

Digital (37, 139, 30)-net over F₂, using

t-expansion [i] based on digital (36, 139, 30)-net over F₂, using
- net from sequence [i] based on digital (36, 29)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 36 and N(F) ≥ 30, using
    - Drinfeld modules of rank 1 [i]

(139−102, 139, 57)-Net in Base 2 — Upper bound on s

There is no (37, 139, 58)-net in base 2, because

29 times m-reduction [i] would yield (37, 110, 58)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹¹⁰, 58, S₂, 2, 73), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 62307 562302 417931 542365 955950 641152 / 37 > 2¹¹⁰ [i]