MinT - Best Known (188−71, 188, s)-Nets in Base 2

Best Known (188−71, 188, s)-Nets in Base 2

(188−71, 188, 68)-Net over F₂ — Constructive and digital

Digital (117, 188, 68)-net over F₂, using

4 times m-reduction [i] based on digital (117, 192, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 96, 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]

(188−71, 188, 100)-Net over F₂ — Digital

Digital (117, 188, 100)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−71, 188, 514)-Net in Base 2 — Upper bound on s

There is no (117, 188, 515)-net in base 2, because

1 times m-reduction [i] would yield (117, 187, 515)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 201 929641 554231 788938 750904 973065 459299 608263 718570 788256 > 2¹⁸⁷ [i]