MinT - Best Known (191−111, 191, s)-Nets in Base 4

Best Known (191−111, 191, s)-Nets in Base 4

(191−111, 191, 104)-Net over F₄ — Constructive and digital

Digital (80, 191, 104)-net over F₄, using

t-expansion [i] based on digital (73, 191, 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]

(191−111, 191, 112)-Net over F₄ — Digital

Digital (80, 191, 112)-net over F₄, using

t-expansion [i] based on digital (73, 191, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(191−111, 191, 810)-Net in Base 4 — Upper bound on s

There is no (80, 191, 811)-net in base 4, because

1 times m-reduction [i] would yield (80, 190, 811)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 560989 148663 763182 031483 389673 432328 053014 658061 011216 708538 583509 478109 167871 915297 536855 795632 579229 007696 005120 > 4¹⁹⁰ [i]