MinT - Best Known (117, 117+72, s)-Nets in Base 2

Best Known (117, 117+72, s)-Nets in Base 2

(117, 117+72, 68)-Net over F₂ — Constructive and digital

Digital (117, 189, 68)-net over F₂, using

3 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]

(117, 117+72, 98)-Net over F₂ — Digital

Digital (117, 189, 98)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+72, 492)-Net in Base 2 — Upper bound on s

There is no (117, 189, 493)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 826 549700 233338 641863 536280 181198 348829 075136 349974 393081 > 2¹⁸⁹ [i]