MinT - Best Known (108−82, 108, s)-Nets in Base 2

Best Known (108−82, 108, s)-Nets in Base 2

(108−82, 108, 21)-Net over F₂ — Constructive and digital

Digital (26, 108, 21)-net over F₂, using

t-expansion [i] based on digital (21, 108, 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]

(108−82, 108, 24)-Net over F₂ — Digital

Digital (26, 108, 24)-net over F₂, using

t-expansion [i] based on digital (25, 108, 24)-net over F₂, using
- net from sequence [i] based on digital (25, 23)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 25 and N(F) ≥ 24, using
    - Drinfeld modules of rank 1 [i]

(108−82, 108, 36)-Net in Base 2 — Upper bound on s

There is no (26, 108, 37)-net in base 2, because

3 times m-reduction [i] would yield (26, 105, 37)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁰⁵, 37, S₂, 3, 79), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 223 106505 640168 374663 419764 146176 / 5 > 2¹⁰⁵ [i]