MinT - Best Known (12, 46, s)-Nets in Base 4

Best Known (12, 46, s)-Nets in Base 4

(12, 46, 28)-Net over F₄ — Constructive and digital

Digital (12, 46, 28)-net over F₄, using

net from sequence [i] based on digital (12, 27)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]

(12, 46, 29)-Net over F₄ — Digital

Digital (12, 46, 29)-net over F₄, using

net from sequence [i] based on digital (12, 28)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 29, using
  - a curve from the manYPoints database [i]

(12, 46, 65)-Net in Base 4 — Upper bound on s

There is no (12, 46, 66)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁶, 66, S₄, 34), but
- the linear programming bound shows that MÂ â‰¥ 571436 608173 282162 524289 857732 214784 / 105 347305 > 4⁴⁶ [i]