MinT - Best Known (82−60, 82, s)-Nets in Base 2

Best Known (82−60, 82, s)-Nets in Base 2

(82−60, 82, 21)-Net over F₂ — Constructive and digital

Digital (22, 82, 21)-net over F₂, using

t-expansion [i] based on digital (21, 82, 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]

(82−60, 82, 36)-Net in Base 2 — Upper bound on s

There is no (22, 82, 37)-net in base 2, because

14 times m-reduction [i] would yield (22, 68, 37)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁶⁸, 37, S₂, 2, 46), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 14167 099448 608935 641088 / 47 > 2⁶⁸ [i]