MinT - Best Known (260−84, 260, s)-Nets in Base 2

Best Known (260−84, 260, s)-Nets in Base 2

(260−84, 260, 112)-Net over F₂ — Constructive and digital

Digital (176, 260, 112)-net over F₂, using

t-expansion [i] based on digital (163, 260, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 130, 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]

(260−84, 260, 188)-Net over F₂ — Digital

Digital (176, 260, 188)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−84, 260, 1144)-Net in Base 2 — Upper bound on s

There is no (176, 260, 1145)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 861057 796767 284243 972842 925293 604145 445622 821027 171426 199231 352474 614349 722036 > 2²⁶⁰ [i]