MinT - Best Known (254−84, 254, s)-Nets in Base 2

Best Known (254−84, 254, s)-Nets in Base 2

(254−84, 254, 112)-Net over F₂ — Constructive and digital

Digital (170, 254, 112)-net over F₂, using

t-expansion [i] based on digital (163, 254, 112)-net over F₂, using
- 6 times m-reduction [i] based on digital (163, 260, 112)-net over F₂, using
  - trace code for nets [i] based on digital (33, 130, 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]

(254−84, 254, 175)-Net over F₂ — Digital

Digital (170, 254, 175)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−84, 254, 1031)-Net in Base 2 — Upper bound on s

There is no (170, 254, 1032)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 29709 442345 640943 881833 951764 131918 922719 576801 033167 650014 595177 849844 938880 > 2²⁵⁴ [i]