MinT - Best Known (234−157, 234, s)-Nets in Base 4

Best Known (234−157, 234, s)-Nets in Base 4

(234−157, 234, 104)-Net over F₄ — Constructive and digital

Digital (77, 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]

(234−157, 234, 112)-Net over F₄ — Digital

Digital (77, 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]

(234−157, 234, 563)-Net in Base 4 — Upper bound on s

There is no (77, 234, 564)-net in base 4, because

1 times m-reduction [i] would yield (77, 233, 564)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 199 227306 762432 673095 500101 939441 746800 270351 137200 782608 474418 554669 142939 817815 060105 330621 895933 952068 507517 822157 514220 886630 222352 973600 > 4²³³ [i]