MinT - Best Known (179−143, 179, s)-Nets in Base 2

Best Known (179−143, 179, s)-Nets in Base 2

(179−143, 179, 24)-Net over F₂ — Constructive and digital

Digital (36, 179, 24)-net over F₂, using

t-expansion [i] based on digital (33, 179, 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]

(179−143, 179, 30)-Net over F₂ — Digital

Digital (36, 179, 30)-net over F₂, using

net from sequence [i] based on digital (36, 29)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 36 and N(F) ≥ 30, using
  - Drinfeld modules of rank 1 [i]

(179−143, 179, 45)-Net in Base 2 — Upper bound on s

There is no (36, 179, 46)-net in base 2, because

2 times m-reduction [i] would yield (36, 177, 46)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁷⁷, 46, S₂, 4, 141), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 13 792459 867792 999725 225123 244352 782652 568652 099652 419584 / 71 > 2¹⁷⁷ [i]