MinT - Best Known (225−104, 225, s)-Nets in Base 2

Best Known (225−104, 225, s)-Nets in Base 2

(225−104, 225, 59)-Net over F₂ — Constructive and digital

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]

(225−104, 225, 80)-Net over F₂ — Digital

Digital (121, 225, 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]

(225−104, 225, 262)-Net in Base 2 — Upper bound on s

There is no (121, 225, 263)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²²⁵, 263, S₂, 104), but
- the linear programming bound shows that MÂ â‰¥ 750 592793 409885 417620 674030 082241 990093 860084 678196 389827 655231 101620 535601 135616 / 12 955120 739875 > 2²²⁵ [i]