MinT - Best Known (214−85, 214, s)-Nets in Base 2

Best Known (214−85, 214, s)-Nets in Base 2

(214−85, 214, 68)-Net over F₂ — Constructive and digital

Digital (129, 214, 68)-net over F₂, using

2 times m-reduction [i] based on digital (129, 216, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 108, 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]

(214−85, 214, 99)-Net over F₂ — Digital

Digital (129, 214, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−85, 214, 495)-Net in Base 2 — Upper bound on s

There is no (129, 214, 496)-net in base 2, because

1 times m-reduction [i] would yield (129, 213, 496)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13427 917628 315833 559092 855676 008818 040024 081270 677215 161645 478289 > 2²¹³ [i]