MinT - Best Known (250−83, 250, s)-Nets in Base 2

Best Known (250−83, 250, s)-Nets in Base 2

(250−83, 250, 112)-Net over F₂ — Constructive and digital

Digital (167, 250, 112)-net over F₂, using

t-expansion [i] based on digital (163, 250, 112)-net over F₂, using
- 10 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]

(250−83, 250, 171)-Net over F₂ — Digital

Digital (167, 250, 171)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−83, 250, 1027)-Net in Base 2 — Upper bound on s

There is no (167, 250, 1028)-net in base 2, because

1 times m-reduction [i] would yield (167, 249, 1028)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 930 727503 789225 574015 382207 607747 914583 873615 736867 219486 692627 411919 250816 > 2²⁴⁹ [i]