MinT - Best Known (234−143, 234, s)-Nets in Base 4

Best Known (234−143, 234, s)-Nets in Base 4

(234−143, 234, 104)-Net over F₄ — Constructive and digital

Digital (91, 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]

(234−143, 234, 144)-Net over F₄ — Digital

Digital (91, 234, 144)-net over F₄, using

net from sequence [i] based on digital (91, 143)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
  - Drinfeld modules of rank 1 [i]

(234−143, 234, 802)-Net in Base 4 — Upper bound on s

There is no (91, 234, 803)-net in base 4, because

1 times m-reduction [i] would yield (91, 233, 803)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 200 553112 226243 609371 213895 874788 887705 652492 585528 879532 437717 065199 366339 465959 317374 337991 593334 121937 490823 567180 257065 988063 261587 800320 > 4²³³ [i]