MinT - Best Known (81, 81+144, s)-Nets in Base 4

Best Known (81, 81+144, s)-Nets in Base 4

(81, 81+144, 104)-Net over F₄ — Constructive and digital

Digital (81, 225, 104)-net over F₄, using

t-expansion [i] based on digital (73, 225, 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]

(81, 81+144, 129)-Net over F₄ — Digital

Digital (81, 225, 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]

(81, 81+144, 643)-Net in Base 4 — Upper bound on s

There is no (81, 225, 644)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3066 821296 925135 071010 041244 427843 950415 617962 060760 130217 679459 508687 837512 537085 774511 478190 293423 789668 551105 276286 448729 561810 627920 > 4²²⁵ [i]