MinT - Best Known (245−88, 245, s)-Nets in Base 2

Best Known (245−88, 245, s)-Nets in Base 2

(245−88, 245, 112)-Net over F₂ — Constructive and digital

Digital (157, 245, 112)-net over F₂, using

3 times m-reduction [i] based on digital (157, 248, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 124, 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]

(245−88, 245, 140)-Net over F₂ — Digital

Digital (157, 245, 140)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−88, 245, 755)-Net in Base 2 — Upper bound on s

There is no (157, 245, 756)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 58 155933 044406 836715 141912 578883 793562 263547 799402 066249 416786 916802 902980 > 2²⁴⁵ [i]