MinT - Best Known (105−82, 105, s)-Nets in Base 2

Best Known (105−82, 105, s)-Nets in Base 2

(105−82, 105, 21)-Net over F₂ — Constructive and digital

Digital (23, 105, 21)-net over F₂, using

t-expansion [i] based on digital (21, 105, 21)-net over F₂, using
- net from sequence [i] based on digital (21, 20)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(105−82, 105, 22)-Net over F₂ — Digital

Digital (23, 105, 22)-net over F₂, using

net from sequence [i] based on digital (23, 21)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 23 and N(F) ≥ 22, using
  - Drinfeld modules of rank 1 [i]

(105−82, 105, 33)-Net in Base 2 — Upper bound on s

There is no (23, 105, 34)-net in base 2, because

11 times m-reduction [i] would yield (23, 94, 34)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁹⁴, 34, S₂, 3, 71), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 188166 885971 377801 784666 882048 / 9 > 2⁹⁴ [i]