MinT - Best Known (124, 222, s)-Nets in Base 2

Best Known (124, 222, s)-Nets in Base 2

(124, 222, 63)-Net over F₂ — Constructive and digital

Digital (124, 222, 63)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (21, 70, 21)-net over F₂, using
  - net from sequence [i] based on digital (21, 20)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]
2. digital (54, 152, 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]

(124, 222, 80)-Net over F₂ — Digital

Digital (124, 222, 80)-net over F₂, using

t-expansion [i] based on digital (121, 222, 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]

(124, 222, 298)-Net in Base 2 — Upper bound on s

There is no (124, 222, 299)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²²², 299, S₂, 98), but
- 1 times code embedding in larger space [i] would yield OA(2²²³, 300, S₂, 98), but
  - the linear programming bound shows that MÂ â‰¥ 1 797227 776840 883681 896516 291018 079602 556004 736527 384481 376471 307374 972535 986485 205069 933364 379648 / 112622 624143 760877 566730 935625 > 2²²³ [i]