MinT - Best Known (234−155, 234, s)-Nets in Base 4

Best Known (234−155, 234, s)-Nets in Base 4

(234−155, 234, 104)-Net over F₄ — Constructive and digital

Digital (79, 234, 104)-net over F₄, using

t-expansion [i] based on digital (73, 234, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(234−155, 234, 112)-Net over F₄ — Digital

Digital (79, 234, 112)-net over F₄, using

t-expansion [i] based on digital (73, 234, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(234−155, 234, 590)-Net in Base 4 — Upper bound on s

There is no (79, 234, 591)-net in base 4, because

1 times m-reduction [i] would yield (79, 233, 591)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 197 047157 447929 255633 102167 871982 978492 651272 858851 202570 400373 057221 289540 124162 605831 841279 029846 496688 994238 835911 842976 904359 650140 142742 > 4²³³ [i]