MinT - Best Known (126−108, 126, s)-Nets in Base 3

Best Known (126−108, 126, s)-Nets in Base 3

(126−108, 126, 28)-Net over F₃ — Constructive and digital

Digital (18, 126, 28)-net over F₃, using

t-expansion [i] based on digital (15, 126, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(126−108, 126, 49)-Net in Base 3 — Upper bound on s

There is no (18, 126, 50)-net in base 3, because

30 times m-reduction [i] would yield (18, 96, 50)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3⁹⁶, 50, S₃, 2, 78), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 629905 858672 458293 489008 047491 314888 858131 415779 / 79 > 3⁹⁶ [i]