MinT - Best Known (216−66, 216, s)-Nets in Base 2

Best Known (216−66, 216, s)-Nets in Base 2

(216−66, 216, 112)-Net over F₂ — Constructive and digital

Digital (150, 216, 112)-net over F₂, using

18 times m-reduction [i] based on digital (150, 234, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 117, 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]

(216−66, 216, 182)-Net over F₂ — Digital

Digital (150, 216, 182)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−66, 216, 1181)-Net in Base 2 — Upper bound on s

There is no (150, 216, 1182)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 107064 422804 176189 488901 000299 988793 998565 071885 438128 303455 651580 > 2²¹⁶ [i]