MinT - Best Known (216−70, 216, s)-Nets in Base 2

Best Known (216−70, 216, s)-Nets in Base 2

(216−70, 216, 112)-Net over F₂ — Constructive and digital

Digital (146, 216, 112)-net over F₂, using

10 times m-reduction [i] based on digital (146, 226, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 113, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(216−70, 216, 159)-Net over F₂ — Digital

Digital (146, 216, 159)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−70, 216, 951)-Net in Base 2 — Upper bound on s

There is no (146, 216, 952)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 106724 045667 427286 017163 363581 313126 116786 419183 429994 997869 534255 > 2²¹⁶ [i]