MinT - Best Known (128−111, 128, s)-Nets in Base 3

Best Known (128−111, 128, s)-Nets in Base 3

(128−111, 128, 28)-Net over F₃ — Constructive and digital

Digital (17, 128, 28)-net over F₃, using

t-expansion [i] based on digital (15, 128, 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]

(128−111, 128, 47)-Net in Base 3 — Upper bound on s

There is no (17, 128, 48)-net in base 3, because

37 times m-reduction [i] would yield (17, 91, 48)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3⁹¹, 48, S₃, 2, 74), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 706 965049 015104 706497 203195 837614 914543 357369 / 25 > 3⁹¹ [i]