MinT - Best Known (174, 174+83, s)-Nets in Base 2

Best Known (174, 174+83, s)-Nets in Base 2

(174, 174+83, 112)-Net over F₂ — Constructive and digital

Digital (174, 257, 112)-net over F₂, using

t-expansion [i] based on digital (163, 257, 112)-net over F₂, using
- 3 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]

(174, 174+83, 186)-Net over F₂ — Digital

Digital (174, 257, 186)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 174+83, 1163)-Net in Base 2 — Upper bound on s

There is no (174, 257, 1164)-net in base 2, because

1 times m-reduction [i] would yield (174, 256, 1164)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 117332 338995 575069 367808 269450 313802 188263 146787 883163 574305 509546 103691 158700 > 2²⁵⁶ [i]