MinT - Best Known (214−73, 214, s)-Nets in Base 2

Best Known (214−73, 214, s)-Nets in Base 2

(214−73, 214, 112)-Net over F₂ — Constructive and digital

Digital (141, 214, 112)-net over F₂, using

2 times m-reduction [i] based on digital (141, 216, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 108, 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]

(214−73, 214, 140)-Net over F₂ — Digital

Digital (141, 214, 140)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−73, 214, 810)-Net in Base 2 — Upper bound on s

There is no (141, 214, 811)-net in base 2, because

1 times m-reduction [i] would yield (141, 213, 811)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13379 094557 625945 349498 991471 695099 638294 188399 086263 734658 990994 > 2²¹³ [i]