MinT - Best Known (114, 199, s)-Nets in Base 2

Best Known (114, 199, s)-Nets in Base 2

(114, 199, 60)-Net over F₂ — Constructive and digital

Digital (114, 199, 60)-net over F₂, using

3 times m-reduction [i] based on digital (114, 202, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 101, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(114, 199, 79)-Net over F₂ — Digital

Digital (114, 199, 79)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 199, 374)-Net in Base 2 — Upper bound on s

There is no (114, 199, 375)-net in base 2, because

1 times m-reduction [i] would yield (114, 198, 375)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 410619 283156 368038 612318 265514 246506 642848 566630 794321 991566 > 2¹⁹⁸ [i]