MinT - Best Known (252−164, 252, s)-Nets in Base 4

Best Known (252−164, 252, s)-Nets in Base 4

(252−164, 252, 104)-Net over F₄ — Constructive and digital

Digital (88, 252, 104)-net over F₄, using

t-expansion [i] based on digital (73, 252, 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]

(252−164, 252, 129)-Net over F₄ — Digital

Digital (88, 252, 129)-net over F₄, using

t-expansion [i] based on digital (81, 252, 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]

(252−164, 252, 674)-Net in Base 4 — Upper bound on s

There is no (88, 252, 675)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 56 420016 306956 154906 655281 684351 588336 332721 591449 577130 997255 720546 463747 082357 820273 335691 009140 762438 785012 926268 323575 752145 558514 523593 963978 828548 > 4²⁵² [i]