MinT - Best Known (160−62, 160, s)-Nets in Base 2

Best Known (160−62, 160, s)-Nets in Base 2

(160−62, 160, 66)-Net over F₂ — Constructive and digital

Digital (98, 160, 66)-net over F₂, using

6 times m-reduction [i] based on digital (98, 166, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 83, 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]

(160−62, 160, 82)-Net over F₂ — Digital

Digital (98, 160, 82)-net over F₂, using

trace code for nets [i] based on digital (18, 80, 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]

(160−62, 160, 400)-Net in Base 2 — Upper bound on s

There is no (98, 160, 401)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 522053 376620 608343 938945 427157 229968 362585 280512 > 2¹⁶⁰ [i]