MinT - Best Known (31−17, 31, s)-Nets in Base 4

Best Known (31−17, 31, s)-Nets in Base 4

(31−17, 31, 32)-Net over F₄ — Constructive and digital

Digital (14, 31, 32)-net over F₄, using

1 times m-reduction [i] based on digital (14, 32, 32)-net over F₄, using
- a shift-net [i]

(31−17, 31, 33)-Net over F₄ — Digital

Digital (14, 31, 33)-net over F₄, using

t-expansion [i] based on digital (13, 31, 33)-net over F₄, using
- net from sequence [i] based on digital (13, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 33, using
    - Drinfeld modules of rank 1 [i]

(31−17, 31, 221)-Net in Base 4 — Upper bound on s

There is no (14, 31, 222)-net in base 4, because

1 times m-reduction [i] would yield (14, 30, 222)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 192539 753198 096553 > 4³⁰ [i]