MinT - Best Known (169−88, 169, s)-Nets in Base 4

Best Known (169−88, 169, s)-Nets in Base 4

(169−88, 169, 104)-Net over F₄ — Constructive and digital

Digital (81, 169, 104)-net over F₄, using

t-expansion [i] based on digital (73, 169, 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]

(169−88, 169, 129)-Net over F₄ — Digital

Digital (81, 169, 129)-net over F₄, using

net from sequence [i] based on digital (81, 128)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
  - Drinfeld modules of rank 1 [i]

(169−88, 169, 1145)-Net in Base 4 — Upper bound on s

There is no (81, 169, 1146)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 575247 094814 142187 730606 372627 778476 196861 166775 007878 278268 873061 872164 159782 315155 783799 015396 261724 > 4¹⁶⁹ [i]