MinT - Best Known (215−70, 215, s)-Nets in Base 2

Best Known (215−70, 215, s)-Nets in Base 2

(215−70, 215, 112)-Net over F₂ — Constructive and digital

Digital (145, 215, 112)-net over F₂, using

9 times m-reduction [i] based on digital (145, 224, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 112, 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]

(215−70, 215, 157)-Net over F₂ — Digital

Digital (145, 215, 157)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−70, 215, 931)-Net in Base 2 — Upper bound on s

There is no (145, 215, 932)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 52683 423324 289589 430698 286054 737974 638987 020616 792638 350293 804747 > 2²¹⁵ [i]