MinT - Best Known (189−60, 189, s)-Nets in Base 2

Best Known (189−60, 189, s)-Nets in Base 2

(189−60, 189, 112)-Net over F₂ — Constructive and digital

Digital (129, 189, 112)-net over F₂, using

3 times m-reduction [i] based on digital (129, 192, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 96, 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]

(189−60, 189, 149)-Net over F₂ — Digital

Digital (129, 189, 149)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−60, 189, 905)-Net in Base 2 — Upper bound on s

There is no (129, 189, 906)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 798 273323 393071 573969 465950 086994 735536 979114 368107 589184 > 2¹⁸⁹ [i]