MinT - Best Known (247−212, 247, s)-Nets in Base 3

Best Known (247−212, 247, s)-Nets in Base 3

(247−212, 247, 38)-Net over F₃ — Constructive and digital

Digital (35, 247, 38)-net over F₃, using

t-expansion [i] based on digital (32, 247, 38)-net over F₃, using
- net from sequence [i] based on digital (32, 37)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
    - an explicitly constructive algebraic function field [i]

(247−212, 247, 47)-Net over F₃ — Digital

Digital (35, 247, 47)-net over F₃, using

net from sequence [i] based on digital (35, 46)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 35 and N(F) ≥ 47, using
  - a curve from the manYPoints database [i]

(247−212, 247, 82)-Net in Base 3 — Upper bound on s

There is no (35, 247, 83)-net in base 3, because

3 times m-reduction [i] would yield (35, 244, 83)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3²⁴⁴, 83, S₃, 3, 209), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 10201 188170 857432 109740 595258 545710 288544 796471 353614 760006 450674 244943 149965 642473 386639 339099 306924 664553 461402 878359 / 35 > 3²⁴⁴ [i]