MinT - Best Known (225−72, 225, s)-Nets in Base 2

Best Known (225−72, 225, s)-Nets in Base 2

(225−72, 225, 112)-Net over F₂ — Constructive and digital

Digital (153, 225, 112)-net over F₂, using

15 times m-reduction [i] based on digital (153, 240, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 120, 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]

(225−72, 225, 169)-Net over F₂ — Digital

Digital (153, 225, 169)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−72, 225, 1034)-Net in Base 2 — Upper bound on s

There is no (153, 225, 1035)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 54 754261 434743 892787 573984 903996 308427 287085 359512 504003 893612 639424 > 2²²⁵ [i]