MinT - Best Known (84, 84+88, s)-Nets in Base 4

Best Known (84, 84+88, s)-Nets in Base 4

(84, 84+88, 104)-Net over F₄ — Constructive and digital

Digital (84, 172, 104)-net over F₄, using

t-expansion [i] based on digital (73, 172, 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]

(84, 84+88, 129)-Net over F₄ — Digital

Digital (84, 172, 129)-net over F₄, using

t-expansion [i] based on digital (81, 172, 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]

(84, 84+88, 1262)-Net in Base 4 — Upper bound on s

There is no (84, 172, 1263)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36 677358 977783 126018 440725 265747 659641 563473 789402 982787 165427 764370 446343 809451 343867 128114 290420 299345 > 4¹⁷² [i]