MinT - Best Known (55, 189, s)-Nets in Base 2

Best Known (55, 189, s)-Nets in Base 2

(55, 189, 42)-Net over F₂ — Constructive and digital

Digital (55, 189, 42)-net over F₂, using

t-expansion [i] based on digital (54, 189, 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]

(55, 189, 82)-Net in Base 2 — Upper bound on s

There is no (55, 189, 83)-net in base 2, because

30 times m-reduction [i] would yield (55, 159, 83)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁵⁹, 83, S₂, 2, 104), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 23 384026 197294 446691 258957 323460 528314 494920 687616 / 21 > 2¹⁵⁹ [i]