MinT - Best Known (84−33, 84, s)-Nets in Base 2

Best Known (84−33, 84, s)-Nets in Base 2

(84−33, 84, 44)-Net over F₂ — Constructive and digital

Digital (51, 84, 44)-net over F₂, using

trace code for nets [i] based on digital (9, 42, 22)-net over F₄, using
- net from sequence [i] based on digital (9, 21)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
    - an explicitly constructive algebraic function field [i]

(84−33, 84, 52)-Net over F₂ — Digital

Digital (51, 84, 52)-net over F₂, using

trace code for nets [i] based on digital (9, 42, 26)-net over F₄, using
- net from sequence [i] based on digital (9, 25)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 26, using
    - Drinfeld modules of rank 1 [i]

(84−33, 84, 225)-Net in Base 2 — Upper bound on s

There is no (51, 84, 226)-net in base 2, because

1 times m-reduction [i] would yield (51, 83, 226)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10 133665 261662 466901 339226 > 2⁸³ [i]