MinT - Best Known (123−81, 123, s)-Nets in Base 2

Best Known (123−81, 123, s)-Nets in Base 2

(123−81, 123, 33)-Net over F₂ — Constructive and digital

Digital (42, 123, 33)-net over F₂, using

t-expansion [i] based on digital (39, 123, 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]

(123−81, 123, 64)-Net in Base 2 — Upper bound on s

There is no (42, 123, 65)-net in base 2, because

extracting embedded OOA [i] would yield OOA(2¹²³, 65, S₂, 2, 81), but
- the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 510 423550 381407 695195 061911 147652 317184 / 41 > 2¹²³ [i]