MinT - Best Known (89, 89+136, s)-Nets in Base 4

Best Known (89, 89+136, s)-Nets in Base 4

(89, 89+136, 104)-Net over F₄ — Constructive and digital

Digital (89, 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]

(89, 89+136, 129)-Net over F₄ — Digital

Digital (89, 225, 129)-net over F₄, using

t-expansion [i] based on 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]

(89, 89+136, 801)-Net in Base 4 — Upper bound on s

There is no (89, 225, 802)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3060 967576 345395 201153 059910 747782 880979 562595 442170 566914 250466 768124 233114 266648 279471 602649 223851 350741 159912 301304 377072 507234 010976 > 4²²⁵ [i]