MinT - Best Known (244−101, 244, s)-Nets in Base 2

Best Known (244−101, 244, s)-Nets in Base 2

(244−101, 244, 75)-Net over F₂ — Constructive and digital

Digital (143, 244, 75)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 89, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (54, 155, 42)-net over F₂, using
  - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
      - an explicitly constructive algebraic function field [i]

(244−101, 244, 101)-Net over F₂ — Digital

Digital (143, 244, 101)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−101, 244, 495)-Net in Base 2 — Upper bound on s

There is no (143, 244, 496)-net in base 2, because

1 times m-reduction [i] would yield (143, 243, 496)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14 783422 984192 431919 149099 538879 997883 379987 833130 367209 845840 543028 339676 > 2²⁴³ [i]