MinT - Best Known (86, 86+121, s)-Nets in Base 4

Best Known (86, 86+121, s)-Nets in Base 4

(86, 86+121, 104)-Net over F₄ — Constructive and digital

Digital (86, 207, 104)-net over F₄, using

t-expansion [i] based on digital (73, 207, 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]

(86, 86+121, 129)-Net over F₄ — Digital

Digital (86, 207, 129)-net over F₄, using

t-expansion [i] based on digital (81, 207, 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]

(86, 86+121, 853)-Net in Base 4 — Upper bound on s

There is no (86, 207, 854)-net in base 4, because

1 times m-reduction [i] would yield (86, 206, 854)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10806 742375 388647 410773 761873 067216 808807 880912 016660 822534 334879 458771 150058 883924 079500 034453 162062 685548 939076 623635 308056 > 4²⁰⁶ [i]