MinT - Best Known (168−50, 168, s)-Nets in Base 2

Best Known (168−50, 168, s)-Nets in Base 2

(168−50, 168, 112)-Net over F₂ — Constructive and digital

Digital (118, 168, 112)-net over F₂, using

2 times m-reduction [i] based on digital (118, 170, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 85, 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]

(168−50, 168, 157)-Net over F₂ — Digital

Digital (118, 168, 157)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−50, 168, 1036)-Net in Base 2 — Upper bound on s

There is no (118, 168, 1037)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 379 036816 118000 953611 170713 809179 100020 535164 462208 > 2¹⁶⁸ [i]