MinT - Best Known (124, 124+105, s)-Nets in Base 2

Best Known (124, 124+105, s)-Nets in Base 2

(124, 124+105, 59)-Net over F₂ — Constructive and digital

Digital (124, 229, 59)-net over F₂, using

5 times m-reduction [i] based on digital (124, 234, 59)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 70, 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, 164, 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, 124+105, 80)-Net over F₂ — Digital

Digital (124, 229, 80)-net over F₂, using

t-expansion [i] based on digital (121, 229, 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, 124+105, 274)-Net in Base 2 — Upper bound on s

There is no (124, 229, 275)-net in base 2, because

1 times m-reduction [i] would yield (124, 228, 275)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2²²⁸, 275, S₂, 104), but
  - the linear programming bound shows that MÂ â‰¥ 251264 125746 691665 140945 653724 331420 478748 637190 708022 716362 001460 206075 835028 865024 / 507 147920 958861 > 2²²⁸ [i]