MinT - Best Known (194−101, 194, s)-Nets in Base 4

Best Known (194−101, 194, s)-Nets in Base 4

(194−101, 194, 104)-Net over F₄ — Constructive and digital

Digital (93, 194, 104)-net over F₄, using

t-expansion [i] based on digital (73, 194, 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]

(194−101, 194, 144)-Net over F₄ — Digital

Digital (93, 194, 144)-net over F₄, using

t-expansion [i] based on digital (91, 194, 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]

(194−101, 194, 1328)-Net in Base 4 — Upper bound on s

There is no (93, 194, 1329)-net in base 4, because

1 times m-reduction [i] would yield (93, 193, 1329)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 160 055790 309017 774798 993974 609600 204605 926718 667086 806593 367114 105806 777002 342150 761424 075718 743927 048550 545551 505040 > 4¹⁹³ [i]