MinT - Best Known (172−52, 172, s)-Nets in Base 2

Best Known (172−52, 172, s)-Nets in Base 2

(172−52, 172, 112)-Net over F₂ — Constructive and digital

Digital (120, 172, 112)-net over F₂, using

2 times m-reduction [i] based on digital (120, 174, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 87, 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]

(172−52, 172, 155)-Net over F₂ — Digital

Digital (120, 172, 155)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−52, 172, 996)-Net in Base 2 — Upper bound on s

There is no (120, 172, 997)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6043 508379 848392 421016 869187 070722 524228 274903 020968 > 2¹⁷² [i]