MinT - Best Known (40, 40+120, s)-Nets in Base 2

Best Known (40, 40+120, s)-Nets in Base 2

(40, 40+120, 33)-Net over F₂ — Constructive and digital

Digital (40, 160, 33)-net over F₂, using

t-expansion [i] based on digital (39, 160, 33)-net over F₂, using
- net from sequence [i] based on digital (39, 32)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(40, 40+120, 53)-Net in Base 2 — Upper bound on s

There is no (40, 160, 54)-net in base 2, because

5 times m-reduction [i] would yield (40, 155, 54)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁵⁵, 54, S₂, 3, 115), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1 826877 046663 628647 754606 040895 353774 569915 678720 / 29 > 2¹⁵⁵ [i]