MinT - Best Known (209−111, 209, s)-Nets in Base 4

Best Known (209−111, 209, s)-Nets in Base 4

(209−111, 209, 104)-Net over F₄ — Constructive and digital

Digital (98, 209, 104)-net over F₄, using

t-expansion [i] based on digital (73, 209, 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]

(209−111, 209, 144)-Net over F₄ — Digital

Digital (98, 209, 144)-net over F₄, using

t-expansion [i] based on digital (91, 209, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(209−111, 209, 1300)-Net in Base 4 — Upper bound on s

There is no (98, 209, 1301)-net in base 4, because

1 times m-reduction [i] would yield (98, 208, 1301)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 170294 774571 630203 263923 241400 931865 675717 410877 389938 579245 416979 901065 213214 915356 266020 992825 333151 123640 905626 564074 356992 > 4²⁰⁸ [i]