MinT - Best Known (42, 42+217, s)-Nets in Base 2

Best Known (42, 42+217, s)-Nets in Base 2

(42, 42+217, 33)-Net over F₂ — Constructive and digital

Digital (42, 259, 33)-net over F₂, using

t-expansion [i] based on digital (39, 259, 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]

(42, 42+217, 51)-Net in Base 2 — Upper bound on s

There is no (42, 259, 52)-net in base 2, because

9 times m-reduction [i] would yield (42, 250, 52)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²⁵⁰, 52, S₂, 5, 208), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 388989 049781 609094 001058 777763 560940 444578 854736 136269 820052 821276 583169 884160 / 209 > 2²⁵⁰ [i]