MinT - Best Known (88, 88+152, s)-Nets in Base 4

Best Known (88, 88+152, s)-Nets in Base 4

(88, 88+152, 104)-Net over F₄ — Constructive and digital

Digital (88, 240, 104)-net over F₄, using

t-expansion [i] based on digital (73, 240, 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]

(88, 88+152, 129)-Net over F₄ — Digital

Digital (88, 240, 129)-net over F₄, using

t-expansion [i] based on digital (81, 240, 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]

(88, 88+152, 712)-Net in Base 4 — Upper bound on s

There is no (88, 240, 713)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 378115 249623 871751 976235 639055 105782 028523 213285 019301 497715 269906 383670 627216 361895 517768 516760 748212 781707 172943 786602 762601 060692 927515 594080 > 4²⁴⁰ [i]