MinT - Best Known (25−18, 25, s)-Nets in Base 2

Best Known (25−18, 25, s)-Nets in Base 2

(25−18, 25, 10)-Net over F₂ — Constructive and digital

Digital (7, 25, 10)-net over F₂, using

t-expansion [i] based on digital (6, 25, 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]
- Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]

(25−18, 25, 14)-Net in Base 2 — Upper bound on s

There is no (7, 25, 15)-net in base 2, because

3 times m-reduction [i] would yield (7, 22, 15)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²², 15, S₂, 3, 15), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 136613 832584 881917 394944 / 32070 152145 568877 > 2²² [i]