MinT - Best Known (28−17, 28, s)-Nets in Base 4

Best Known (28−17, 28, s)-Nets in Base 4

(28−17, 28, 27)-Net over F₄ — Constructive and digital

Digital (11, 28, 27)-net over F₄, using

t-expansion [i] based on digital (10, 28, 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]

(28−17, 28, 129)-Net in Base 4 — Upper bound on s

There is no (11, 28, 130)-net in base 4, because

1 times m-reduction [i] would yield (11, 27, 130)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 19109 270377 581424 > 4²⁷ [i]