MinT - Best Known (92, 92+46, s)-Nets in Base 2

Best Known (92, 92+46, s)-Nets in Base 2

(92, 92+46, 68)-Net over F₂ — Constructive and digital

Digital (92, 138, 68)-net over F₂, using

4 times m-reduction [i] based on digital (92, 142, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 71, 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]

(92, 92+46, 103)-Net over F₂ — Digital

Digital (92, 138, 103)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 92+46, 570)-Net in Base 2 — Upper bound on s

There is no (92, 138, 571)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 358010 530745 514343 385444 454396 338490 066228 > 2¹³⁸ [i]