MinT - Best Known (245−82, 245, s)-Nets in Base 2

Best Known (245−82, 245, s)-Nets in Base 2

(245−82, 245, 112)-Net over F₂ — Constructive and digital

Digital (163, 245, 112)-net over F₂, using

15 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]

(245−82, 245, 165)-Net over F₂ — Digital

Digital (163, 245, 165)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−82, 245, 956)-Net in Base 2 — Upper bound on s

There is no (163, 245, 957)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 58 183512 031938 882638 376287 847658 379445 495760 487459 331060 358859 136184 977810 > 2²⁴⁵ [i]