MinT - Best Known (37, 37+34, s)-Nets in Base 2

Best Known (37, 37+34, s)-Nets in Base 2

(37, 37+34, 26)-Net over F₂ — Constructive and digital

Digital (37, 71, 26)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 26, 12)-net over F₂, using
  - net from sequence [i] based on digital (9, 11)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 9 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (11, 45, 14)-net over F₂, using
  - net from sequence [i] based on digital (11, 13)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]

(37, 37+34, 30)-Net over F₂ — Digital

Digital (37, 71, 30)-net over F₂, using

t-expansion [i] based on digital (36, 71, 30)-net over F₂, using
- net from sequence [i] based on digital (36, 29)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 36 and N(F) ≥ 30, using
    - Drinfeld modules of rank 1 [i]

(37, 37+34, 91)-Net in Base 2 — Upper bound on s

There is no (37, 71, 92)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2⁷¹, 92, S₂, 34), but
- the linear programming bound shows that MÂ â‰¥ 759 205414 717987 121715 478528 / 311025 > 2⁷¹ [i]