MinT - Best Known (219−64, 219, s)-Nets in Base 2

Best Known (219−64, 219, s)-Nets in Base 2

(219−64, 219, 135)-Net over F₂ — Constructive and digital

Digital (155, 219, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 73, 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]

(219−64, 219, 205)-Net over F₂ — Digital

Digital (155, 219, 205)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−64, 219, 1422)-Net in Base 2 — Upper bound on s

There is no (155, 219, 1423)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 855423 409495 032964 232690 290039 117282 823599 221342 214011 573782 236164 > 2²¹⁹ [i]