MinT - Best Known (248−86, 248, s)-Nets in Base 2

Best Known (248−86, 248, s)-Nets in Base 2

(248−86, 248, 112)-Net over F₂ — Constructive and digital

Digital (162, 248, 112)-net over F₂, using

10 times m-reduction [i] based on digital (162, 258, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 129, 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]

(248−86, 248, 153)-Net over F₂ — Digital

Digital (162, 248, 153)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−86, 248, 857)-Net in Base 2 — Upper bound on s

There is no (162, 248, 858)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 459 664702 920486 881352 157799 704095 244066 932680 812076 497208 544956 604834 170280 > 2²⁴⁸ [i]