MinT - Best Known (248−88, 248, s)-Nets in Base 2

Best Known (248−88, 248, s)-Nets in Base 2

(248−88, 248, 112)-Net over F₂ — Constructive and digital

Digital (160, 248, 112)-net over F₂, using

6 times m-reduction [i] based on digital (160, 254, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 127, 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]

(248−88, 248, 146)-Net over F₂ — Digital

Digital (160, 248, 146)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−88, 248, 794)-Net in Base 2 — Upper bound on s

There is no (160, 248, 795)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 452 441155 101380 529401 842828 028916 943670 059422 463328 263453 069056 781671 929184 > 2²⁴⁸ [i]