MinT - Best Known (187−97, 187, s)-Nets in Base 4

Best Known (187−97, 187, s)-Nets in Base 4

(187−97, 187, 104)-Net over F₄ — Constructive and digital

Digital (90, 187, 104)-net over F₄, using

t-expansion [i] based on digital (73, 187, 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]

(187−97, 187, 129)-Net over F₄ — Digital

Digital (90, 187, 129)-net over F₄, using

t-expansion [i] based on digital (81, 187, 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]

(187−97, 187, 1305)-Net in Base 4 — Upper bound on s

There is no (90, 187, 1306)-net in base 4, because

1 times m-reduction [i] would yield (90, 186, 1306)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9717 505684 520965 438870 160665 890723 136984 835543 120431 737796 745108 479267 333694 567972 838132 678187 578594 575819 232760 > 4¹⁸⁶ [i]