MinT - Best Known (39, 75, s)-Nets in Base 2

Best Known (39, 75, s)-Nets in Base 2

(39, 75, 33)-Net over F₂ — Constructive and digital

Digital (39, 75, 33)-net over F₂, using

net from sequence [i] based on digital (39, 32)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]

(39, 75, 95)-Net in Base 2 — Upper bound on s

There is no (39, 75, 96)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2⁷⁵, 96, S₂, 36), but
- the linear programming bound shows that MÂ â‰¥ 22708 462595 641194 417680 809984 / 528333 > 2⁷⁵ [i]