MinT - Best Known (126−102, 126, s)-Nets in Base 2

Best Known (126−102, 126, s)-Nets in Base 2

(126−102, 126, 21)-Net over F₂ — Constructive and digital

Digital (24, 126, 21)-net over F₂, using

t-expansion [i] based on digital (21, 126, 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]

(126−102, 126, 22)-Net over F₂ — Digital

Digital (24, 126, 22)-net over F₂, using

t-expansion [i] based on digital (23, 126, 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]

(126−102, 126, 32)-Net in Base 2 — Upper bound on s

There is no (24, 126, 33)-net in base 2, because

1 times m-reduction [i] would yield (24, 125, 33)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹²⁵, 33, S₂, 4, 101), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 850 705917 302346 158658 436518 579420 528640 / 17 > 2¹²⁵ [i]