MinT - Best Known (259−176, 259, s)-Nets in Base 4

Best Known (259−176, 259, s)-Nets in Base 4

(259−176, 259, 104)-Net over F₄ — Constructive and digital

Digital (83, 259, 104)-net over F₄, using

t-expansion [i] based on digital (73, 259, 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]

(259−176, 259, 129)-Net over F₄ — Digital

Digital (83, 259, 129)-net over F₄, using

t-expansion [i] based on digital (81, 259, 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]

(259−176, 259, 591)-Net in Base 4 — Upper bound on s

There is no (83, 259, 592)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 892510 273732 123217 703637 180572 037762 975213 741450 560469 423285 002934 894936 382018 240580 126312 374524 505467 418217 478248 398084 171651 325857 949345 861503 882030 109280 > 4²⁵⁹ [i]