MinT - Best Known (212−191, 212, s)-Nets in Base 3

Best Known (212−191, 212, s)-Nets in Base 3

(212−191, 212, 32)-Net over F₃ — Constructive and digital

Digital (21, 212, 32)-net over F₃, using

net from sequence [i] based on digital (21, 31)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(212−191, 212, 52)-Net in Base 3 — Upper bound on s

There is no (21, 212, 53)-net in base 3, because

5 times m-reduction [i] would yield (21, 207, 53)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3²⁰⁷, 53, S₃, 4, 186), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 165555 871196 388364 355015 704118 291262 504527 064871 597522 368472 700777 167654 116327 144149 485010 990630 603295 / 187 > 3²⁰⁷ [i]