MinT - Best Known (87, 87+154, s)-Nets in Base 4

Best Known (87, 87+154, s)-Nets in Base 4

(87, 87+154, 104)-Net over F₄ — Constructive and digital

Digital (87, 241, 104)-net over F₄, using

t-expansion [i] based on digital (73, 241, 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]

(87, 87+154, 129)-Net over F₄ — Digital

Digital (87, 241, 129)-net over F₄, using

t-expansion [i] based on digital (81, 241, 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]

(87, 87+154, 691)-Net in Base 4 — Upper bound on s

There is no (87, 241, 692)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 206430 480202 002426 698535 444559 984567 756714 122714 230377 202431 058548 090728 113640 147658 730361 606983 680426 177839 968666 408741 461912 071606 583962 173400 > 4²⁴¹ [i]