MinT - Best Known (223−102, 223, s)-Nets in Base 2

Best Known (223−102, 223, s)-Nets in Base 2

(223−102, 223, 59)-Net over F₂ — Constructive and digital

Digital (121, 223, 59)-net over F₂, using

2 times m-reduction [i] based on digital (121, 225, 59)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 67, 17)-net over F₂, using
    - net from sequence [i] based on digital (15, 16)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
        an explicitly constructive algebraic function field [i]
  2. digital (54, 158, 42)-net over F₂, using
    - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
        an explicitly constructive algebraic function field [i]

(223−102, 223, 80)-Net over F₂ — Digital

Digital (121, 223, 80)-net over F₂, using

net from sequence [i] based on digital (121, 79)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 121 and N(F) ≥ 80, using
  - Drinfeld modules of rank 1 [i]

(223−102, 223, 265)-Net in Base 2 — Upper bound on s

There is no (121, 223, 266)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²²³, 266, S₂, 102), but
- the linear programming bound shows that MÂ â‰¥ 7696 993027 830529 825591 180052 275706 499308 043173 051648 348201 768483 825054 629863 882752 / 565 467550 305957 > 2²²³ [i]