MinT - Best Known (131, 131+86, s)-Nets in Base 2

Best Known (131, 131+86, s)-Nets in Base 2

(131, 131+86, 68)-Net over F₂ — Constructive and digital

Digital (131, 217, 68)-net over F₂, using

3 times m-reduction [i] based on digital (131, 220, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 110, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(131, 131+86, 101)-Net over F₂ — Digital

Digital (131, 217, 101)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+86, 497)-Net in Base 2 — Upper bound on s

There is no (131, 217, 498)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 225071 103919 362786 635713 119608 651371 503567 549423 197010 458778 808128 > 2²¹⁷ [i]