MinT - Best Known (223−145, 223, s)-Nets in Base 4

Best Known (223−145, 223, s)-Nets in Base 4

(223−145, 223, 104)-Net over F₄ — Constructive and digital

Digital (78, 223, 104)-net over F₄, using

t-expansion [i] based on digital (73, 223, 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]

(223−145, 223, 112)-Net over F₄ — Digital

Digital (78, 223, 112)-net over F₄, using

t-expansion [i] based on digital (73, 223, 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]

(223−145, 223, 604)-Net in Base 4 — Upper bound on s

There is no (78, 223, 605)-net in base 4, because

1 times m-reduction [i] would yield (78, 222, 605)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 383223 499574 771916 104786 879790 733984 566568 649481 285442 760983 184070 983940 683458 223490 005828 766422 159882 669169 193992 583009 518976 724301 > 4²²² [i]