MinT - Best Known (188−101, 188, s)-Nets in Base 4

Best Known (188−101, 188, s)-Nets in Base 4

(188−101, 188, 104)-Net over F₄ — Constructive and digital

Digital (87, 188, 104)-net over F₄, using

t-expansion [i] based on digital (73, 188, 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]

(188−101, 188, 129)-Net over F₄ — Digital

Digital (87, 188, 129)-net over F₄, using

t-expansion [i] based on digital (81, 188, 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]

(188−101, 188, 1118)-Net in Base 4 — Upper bound on s

There is no (87, 188, 1119)-net in base 4, because

1 times m-reduction [i] would yield (87, 187, 1119)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38791 070817 404548 035199 059557 872773 858118 386574 123756 961792 299717 292289 485158 080406 156040 284876 672451 946506 886106 > 4¹⁸⁷ [i]