MinT - Best Known (236−102, 236, s)-Nets in Base 2

Best Known (236−102, 236, s)-Nets in Base 2

(236−102, 236, 66)-Net over F₂ — Constructive and digital

Digital (134, 236, 66)-net over F₂, using

2 times m-reduction [i] based on digital (134, 238, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 119, 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]

(236−102, 236, 89)-Net over F₂ — Digital

Digital (134, 236, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−102, 236, 419)-Net in Base 2 — Upper bound on s

There is no (134, 236, 420)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 113782 543099 081274 110825 481909 596814 597067 675720 921023 496615 447667 709768 > 2²³⁶ [i]