MinT - Best Known (215−72, 215, s)-Nets in Base 2

Best Known (215−72, 215, s)-Nets in Base 2

(215−72, 215, 112)-Net over F₂ — Constructive and digital

Digital (143, 215, 112)-net over F₂, using

5 times m-reduction [i] based on digital (143, 220, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 110, 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]

(215−72, 215, 147)-Net over F₂ — Digital

Digital (143, 215, 147)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−72, 215, 844)-Net in Base 2 — Upper bound on s

There is no (143, 215, 845)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 53886 905706 088156 194331 310171 723693 309270 486976 394172 530276 418970 > 2²¹⁵ [i]