MinT - Best Known (219−88, 219, s)-Nets in Base 2

Best Known (219−88, 219, s)-Nets in Base 2

(219−88, 219, 68)-Net over F₂ — Constructive and digital

Digital (131, 219, 68)-net over F₂, using

1 times m-reduction [i] based on digital (131, 220, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 110, 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]

(219−88, 219, 99)-Net over F₂ — Digital

Digital (131, 219, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−88, 219, 481)-Net in Base 2 — Upper bound on s

There is no (131, 219, 482)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 882585 488628 112177 549014 239582 099959 099369 216695 704634 493574 997520 > 2²¹⁹ [i]