MinT - Best Known (12, 12+23, s)-Nets in Base 4

Best Known (12, 12+23, s)-Nets in Base 4

(12, 12+23, 28)-Net over F₄ — Constructive and digital

Digital (12, 35, 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, 12+23, 29)-Net over F₄ — Digital

Digital (12, 35, 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, 12+23, 110)-Net in Base 4 — Upper bound on s

There is no (12, 35, 111)-net in base 4, because

1 times m-reduction [i] would yield (12, 34, 111)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 312 862910 413898 836432 > 4³⁴ [i]