MinT - Best Known (34, 34+163, s)-Nets in Base 2

Best Known (34, 34+163, s)-Nets in Base 2

(34, 34+163, 24)-Net over F₂ — Constructive and digital

Digital (34, 197, 24)-net over F₂, using

t-expansion [i] based on digital (33, 197, 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]

(34, 34+163, 28)-Net over F₂ — Digital

Digital (34, 197, 28)-net over F₂, using

t-expansion [i] based on digital (33, 197, 28)-net over F₂, using
- net from sequence [i] based on digital (33, 27)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 28, using
    - Drinfeld modules of rank 1 [i]

(34, 34+163, 43)-Net in Base 2 — Upper bound on s

There is no (34, 197, 44)-net in base 2, because

28 times m-reduction [i] would yield (34, 169, 44)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁶⁹, 44, S₂, 4, 135), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 14965 776766 268445 882405 732687 014738 121276 749240 074240 / 17 > 2¹⁶⁹ [i]