MinT - Best Known (43−37, 43, s)-Nets in Base 2

Best Known (43−37, 43, s)-Nets in Base 2

(43−37, 43, 10)-Net over F₂ — Constructive and digital

Digital (6, 43, 10)-net over F₂, using

net from sequence [i] based on digital (6, 9)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
  - an explicitly constructive algebraic function field [i]

(43−37, 43, 11)-Net in Base 2 — Upper bound on s

There is no (6, 43, 12)-net in base 2, because

extracting embedded OOA [i] would yield OOA(2⁴³, 12, S₂, 4, 37), but
- the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 175 921860 444160 / 19 > 2⁴³ [i]