MinT - Best Known (162−58, 162, s)-Nets in Base 2

Best Known (162−58, 162, s)-Nets in Base 2

(162−58, 162, 68)-Net over F₂ — Constructive and digital

Digital (104, 162, 68)-net over F₂, using

4 times m-reduction [i] based on digital (104, 166, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 83, 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]

(162−58, 162, 100)-Net over F₂ — Digital

Digital (104, 162, 100)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−58, 162, 519)-Net in Base 2 — Upper bound on s

There is no (104, 162, 520)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 107553 132099 754063 291193 165362 681299 358671 623232 > 2¹⁶² [i]