MinT - Best Known (90, 90+162, s)-Nets in Base 4

Best Known (90, 90+162, s)-Nets in Base 4

(90, 90+162, 104)-Net over F₄ — Constructive and digital

Digital (90, 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]

(90, 90+162, 129)-Net over F₄ — Digital

Digital (90, 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]

(90, 90+162, 705)-Net in Base 4 — Upper bound on s

There is no (90, 252, 706)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53 621233 726371 300613 282678 919944 618178 637449 353048 835452 042772 932438 344334 737133 371783 989153 526978 320839 083088 963825 078814 287308 959743 502619 109879 748536 > 4²⁵² [i]