MinT - Best Known (127, 212, s)-Nets in Base 2

Best Known (127, 212, s)-Nets in Base 2

(127, 212, 68)-Net over F₂ — Constructive and digital

Digital (127, 212, 68)-net over F₂, using

trace code for nets [i] based on digital (21, 106, 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]

(127, 212, 96)-Net over F₂ — Digital

Digital (127, 212, 96)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 212, 477)-Net in Base 2 — Upper bound on s

There is no (127, 212, 478)-net in base 2, because

1 times m-reduction [i] would yield (127, 211, 478)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3341 075594 074241 990804 933285 350711 352988 226213 267754 165450 749324 > 2²¹¹ [i]