MinT - Best Known (37, 37+69, s)-Nets in Base 2

Best Known (37, 37+69, s)-Nets in Base 2

(37, 37+69, 24)-Net over F₂ — Constructive and digital

Digital (37, 106, 24)-net over F₂, using

t-expansion [i] based on digital (33, 106, 24)-net over F₂, using
- net from sequence [i] based on digital (33, 23)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(37, 37+69, 30)-Net over F₂ — Digital

Digital (37, 106, 30)-net over F₂, using

t-expansion [i] based on digital (36, 106, 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+69, 72)-Net in Base 2 — Upper bound on s

There is no (37, 106, 73)-net in base 2, because

1 times m-reduction [i] would yield (37, 105, 73)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 42 355158 274920 354758 162770 840736 > 2¹⁰⁵ [i]