MinT - Best Known (150−41, 150, s)-Nets in Base 2

Best Known (150−41, 150, s)-Nets in Base 2

(150−41, 150, 135)-Net over F₂ — Constructive and digital

Digital (109, 150, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 50, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(150−41, 150, 176)-Net over F₂ — Digital

Digital (109, 150, 176)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−41, 150, 1422)-Net in Base 2 — Upper bound on s

There is no (109, 150, 1423)-net in base 2, because

1 times m-reduction [i] would yield (109, 149, 1423)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 715 457534 858676 145814 803215 245989 611295 360216 > 2¹⁴⁹ [i]