MinT - Best Known (134−49, 134, s)-Nets in Base 2

Best Known (134−49, 134, s)-Nets in Base 2

(134−49, 134, 66)-Net over F₂ — Constructive and digital

Digital (85, 134, 66)-net over F₂, using

6 times m-reduction [i] based on digital (85, 140, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 70, 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]

(134−49, 134, 82)-Net over F₂ — Digital

Digital (85, 134, 82)-net over F₂, using

trace code for nets [i] based on digital (18, 67, 41)-net over F₄, using
- net from sequence [i] based on digital (18, 40)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 18 and N(F) ≥ 41, using
    - Drinfeld modules of rank 1 [i]

(134−49, 134, 422)-Net in Base 2 — Upper bound on s

There is no (85, 134, 423)-net in base 2, because

1 times m-reduction [i] would yield (85, 133, 423)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11271 913406 771145 448422 496433 012124 484964 > 2¹³³ [i]