MinT - Best Known (219−94, 219, s)-Nets in Base 2

Best Known (219−94, 219, s)-Nets in Base 2

(219−94, 219, 66)-Net over F₂ — Constructive and digital

Digital (125, 219, 66)-net over F₂, using

1 times m-reduction [i] based on digital (125, 220, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 110, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(219−94, 219, 85)-Net over F₂ — Digital

Digital (125, 219, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−94, 219, 398)-Net in Base 2 — Upper bound on s

There is no (125, 219, 399)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 865760 931192 034745 740005 818365 750702 950678 796214 480904 505439 001208 > 2²¹⁹ [i]