MinT - Best Known (91, 91+55, s)-Nets in Base 2

Best Known (91, 91+55, s)-Nets in Base 2

(91, 91+55, 66)-Net over F₂ — Constructive and digital

Digital (91, 146, 66)-net over F₂, using

6 times m-reduction [i] based on digital (91, 152, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 76, 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]

(91, 91+55, 82)-Net over F₂ — Digital

Digital (91, 146, 82)-net over F₂, using

trace code for nets [i] based on digital (18, 73, 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]

(91, 91+55, 413)-Net in Base 2 — Upper bound on s

There is no (91, 146, 414)-net in base 2, because

1 times m-reduction [i] would yield (91, 145, 414)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 46 098890 549592 010609 005580 522103 883490 121222 > 2¹⁴⁵ [i]