MinT - Best Known (197−99, 197, s)-Nets in Base 4

Best Known (197−99, 197, s)-Nets in Base 4

(197−99, 197, 104)-Net over F₄ — Constructive and digital

Digital (98, 197, 104)-net over F₄, using

t-expansion [i] based on digital (73, 197, 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]

(197−99, 197, 144)-Net over F₄ — Digital

Digital (98, 197, 144)-net over F₄, using

t-expansion [i] based on digital (91, 197, 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]

(197−99, 197, 1590)-Net in Base 4 — Upper bound on s

There is no (98, 197, 1591)-net in base 4, because

1 times m-reduction [i] would yield (98, 196, 1591)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10104 480335 037255 531789 430942 775037 560037 619693 508081 299146 942079 781179 823326 913590 878114 055162 437498 006305 720724 864382 > 4¹⁹⁶ [i]