MinT - Best Known (127, 234, s)-Nets in Base 2

Best Known (127, 234, s)-Nets in Base 2

(127, 234, 62)-Net over F₂ — Constructive and digital

Digital (127, 234, 62)-net over F₂, using

1 times m-reduction [i] based on digital (127, 235, 62)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (19, 73, 20)-net over F₂, using
    - net from sequence [i] based on digital (19, 19)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
        an explicitly constructive algebraic function field [i]
  2. digital (54, 162, 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]

(127, 234, 81)-Net over F₂ — Digital

Digital (127, 234, 81)-net over F₂, using

t-expansion [i] based on digital (126, 234, 81)-net over F₂, using
- net from sequence [i] based on digital (126, 80)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 126 and N(F) ≥ 81, using
    - Drinfeld modules of rank 1 [i]

(127, 234, 280)-Net in Base 2 — Upper bound on s

There is no (127, 234, 281)-net in base 2, because

1 times m-reduction [i] would yield (127, 233, 281)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2²³³, 281, S₂, 106), but
  - the linear programming bound shows that MÂ â‰¥ 96255 071560 945144 825845 753186 529299 549319 657197 345428 176368 791637 411331 289766 066166 693888 / 6 100003 838212 464375 > 2²³³ [i]