MinT - Best Known (237−151, 237, s)-Nets in Base 4

Best Known (237−151, 237, s)-Nets in Base 4

(237−151, 237, 104)-Net over F₄ — Constructive and digital

Digital (86, 237, 104)-net over F₄, using

t-expansion [i] based on digital (73, 237, 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]

(237−151, 237, 129)-Net over F₄ — Digital

Digital (86, 237, 129)-net over F₄, using

t-expansion [i] based on digital (81, 237, 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]

(237−151, 237, 691)-Net in Base 4 — Upper bound on s

There is no (86, 237, 692)-net in base 4, because

1 times m-reduction [i] would yield (86, 236, 692)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12926 378172 800168 915223 652647 733304 604371 307949 931404 414287 675886 285008 680482 658926 567633 181703 505839 017400 185280 854684 351874 733348 872306 594460 > 4²³⁶ [i]