MinT - Best Known (254−87, 254, s)-Nets in Base 2

Best Known (254−87, 254, s)-Nets in Base 2

(254−87, 254, 112)-Net over F₂ — Constructive and digital

Digital (167, 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]

(254−87, 254, 161)-Net over F₂ — Digital

Digital (167, 254, 161)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−87, 254, 934)-Net in Base 2 — Upper bound on s

There is no (167, 254, 935)-net in base 2, because

1 times m-reduction [i] would yield (167, 253, 935)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14660 404367 239978 386475 775380 254931 509583 088859 906002 081700 624322 693004 469600 > 2²⁵³ [i]