MinT - Best Known (11, 11+13, s)-Nets in Base 4

Best Known (11, 11+13, s)-Nets in Base 4

(11, 11+13, 27)-Net over F₄ — Constructive and digital

Digital (11, 24, 27)-net over F₄, using

t-expansion [i] based on digital (10, 24, 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]

(11, 11+13, 198)-Net in Base 4 — Upper bound on s

There is no (11, 24, 199)-net in base 4, because

1 times m-reduction [i] would yield (11, 23, 199)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 71 824834 624393 > 4²³ [i]