MinT - Best Known (34−27, 34, s)-Nets in Base 2

Best Known (34−27, 34, s)-Nets in Base 2

(34−27, 34, 10)-Net over F₂ — Constructive and digital

Digital (7, 34, 10)-net over F₂, using

t-expansion [i] based on digital (6, 34, 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]

(34−27, 34, 13)-Net in Base 2 — Upper bound on s

There is no (7, 34, 14)-net in base 2, because

8 times m-reduction [i] would yield (7, 26, 14)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²⁶, 14, S₂, 3, 19), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 10 025795 846144 / 143945 > 2²⁶ [i]