MinT - Best Known (33−19, 33, s)-Nets in Base 4

Best Known (33−19, 33, s)-Nets in Base 4

(33−19, 33, 30)-Net over F₄ — Constructive and digital

Digital (14, 33, 30)-net over F₄, using

t-expansion [i] based on digital (13, 33, 30)-net over F₄, using
- net from sequence [i] based on digital (13, 29)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
    - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(33−19, 33, 33)-Net over F₄ — Digital

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

t-expansion [i] based on digital (13, 33, 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]

(33−19, 33, 184)-Net in Base 4 — Upper bound on s

There is no (14, 33, 185)-net in base 4, because

1 times m-reduction [i] would yield (14, 32, 185)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 19 143497 287883 477692 > 4³² [i]