MinT - Best Known (255−86, 255, s)-Nets in Base 2

Best Known (255−86, 255, s)-Nets in Base 2

(255−86, 255, 112)-Net over F₂ — Constructive and digital

Digital (169, 255, 112)-net over F₂, using

t-expansion [i] based on digital (163, 255, 112)-net over F₂, using
- 5 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]

(255−86, 255, 167)-Net over F₂ — Digital

Digital (169, 255, 167)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(255−86, 255, 967)-Net in Base 2 — Upper bound on s

There is no (169, 255, 968)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 59589 048667 187092 999704 458279 326850 343758 312178 748250 713945 141901 219973 301320 > 2²⁵⁵ [i]