MinT - Best Known (166−48, 166, s)-Nets in Base 2

Best Known (166−48, 166, s)-Nets in Base 2

(166−48, 166, 112)-Net over F₂ — Constructive and digital

Digital (118, 166, 112)-net over F₂, using

4 times m-reduction [i] based on digital (118, 170, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 85, 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]

(166−48, 166, 167)-Net over F₂ — Digital

Digital (118, 166, 167)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−48, 166, 1149)-Net in Base 2 — Upper bound on s

There is no (118, 166, 1150)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 94 783225 612099 472903 288712 241531 127693 473688 097821 > 2¹⁶⁶ [i]