MinT - Best Known (216−92, 216, s)-Nets in Base 2

Best Known (216−92, 216, s)-Nets in Base 2

(216−92, 216, 66)-Net over F₂ — Constructive and digital

Digital (124, 216, 66)-net over F₂, using

2 times m-reduction [i] based on digital (124, 218, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 109, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(216−92, 216, 85)-Net over F₂ — Digital

Digital (124, 216, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−92, 216, 402)-Net in Base 2 — Upper bound on s

There is no (124, 216, 403)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 114414 103511 869838 418363 863080 115669 044269 776207 187649 435422 361232 > 2²¹⁶ [i]