MinT - Best Known (82−32, 82, s)-Nets in Base 2

Best Known (82−32, 82, s)-Nets in Base 2

(82−32, 82, 44)-Net over F₂ — Constructive and digital

Digital (50, 82, 44)-net over F₂, using

trace code for nets [i] based on digital (9, 41, 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]

(82−32, 82, 52)-Net over F₂ — Digital

Digital (50, 82, 52)-net over F₂, using

trace code for nets [i] based on digital (9, 41, 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]

(82−32, 82, 214)-Net in Base 2 — Upper bound on s

There is no (50, 82, 215)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4 897536 862934 084367 399753 > 2⁸² [i]