MinT - Best Known (214−66, 214, s)-Nets in Base 2

Best Known (214−66, 214, s)-Nets in Base 2

(214−66, 214, 112)-Net over F₂ — Constructive and digital

Digital (148, 214, 112)-net over F₂, using

16 times m-reduction [i] based on digital (148, 230, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 115, 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]

(214−66, 214, 177)-Net over F₂ — Digital

Digital (148, 214, 177)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−66, 214, 1130)-Net in Base 2 — Upper bound on s

There is no (148, 214, 1131)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26445 159245 089207 366897 392640 900695 992974 499427 348567 424439 891108 > 2²¹⁴ [i]