MinT - Best Known (31−21, 31, s)-Nets in Base 4

Best Known (31−21, 31, s)-Nets in Base 4

(31−21, 31, 27)-Net over F₄ — Constructive and digital

Digital (10, 31, 27)-net over F₄, using

net from sequence [i] based on digital (10, 26)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
  - an explicitly constructive algebraic function field [i]

(31−21, 31, 89)-Net in Base 4 — Upper bound on s

There is no (10, 31, 90)-net in base 4, because

1 times m-reduction [i] would yield (10, 30, 90)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 275618 604557 474928 > 4³⁰ [i]