MinT - Best Known (199−64, 199, s)-Nets in Base 2

Best Known (199−64, 199, s)-Nets in Base 2

(199−64, 199, 112)-Net over F₂ — Constructive and digital

Digital (135, 199, 112)-net over F₂, using

5 times m-reduction [i] based on digital (135, 204, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 102, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(199−64, 199, 151)-Net over F₂ — Digital

Digital (135, 199, 151)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−64, 199, 906)-Net in Base 2 — Upper bound on s

There is no (135, 199, 907)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 826616 374954 762664 516697 022669 899905 248519 747167 593918 792372 > 2¹⁹⁹ [i]