MinT - Best Known (34, 34+88, s)-Nets in Base 2

Best Known (34, 34+88, s)-Nets in Base 2

(34, 34+88, 24)-Net over F₂ — Constructive and digital

Digital (34, 122, 24)-net over F₂, using

t-expansion [i] based on digital (33, 122, 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+88, 28)-Net over F₂ — Digital

Digital (34, 122, 28)-net over F₂, using

t-expansion [i] based on digital (33, 122, 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+88, 53)-Net in Base 2 — Upper bound on s

There is no (34, 122, 54)-net in base 2, because

20 times m-reduction [i] would yield (34, 102, 54)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁰², 54, S₂, 2, 68), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 162 259276 829213 363391 578010 288128 / 23 > 2¹⁰² [i]