MinT - Best Known (229−68, 229, s)-Nets in Base 2

Best Known (229−68, 229, s)-Nets in Base 2

(229−68, 229, 112)-Net over F₂ — Constructive and digital

Digital (161, 229, 112)-net over F₂, using

27 times m-reduction [i] based on digital (161, 256, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 128, 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]

(229−68, 229, 205)-Net over F₂ — Digital

Digital (161, 229, 205)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−68, 229, 1392)-Net in Base 2 — Upper bound on s

There is no (161, 229, 1393)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 874 737542 710071 052594 669281 836810 276079 328345 394482 598971 252253 899420 > 2²²⁹ [i]