MinT - Best Known (178−66, 178, s)-Nets in Base 2

Best Known (178−66, 178, s)-Nets in Base 2

(178−66, 178, 68)-Net over F₂ — Constructive and digital

Digital (112, 178, 68)-net over F₂, using

4 times m-reduction [i] based on digital (112, 182, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 91, 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]

(178−66, 178, 99)-Net over F₂ — Digital

Digital (112, 178, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−66, 178, 506)-Net in Base 2 — Upper bound on s

There is no (112, 178, 507)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 398100 240354 430045 926039 798160 877961 372794 974480 004540 > 2¹⁷⁸ [i]