MinT - Best Known (197−100, 197, s)-Nets in Base 4

Best Known (197−100, 197, s)-Nets in Base 4

(197−100, 197, 104)-Net over F₄ — Constructive and digital

Digital (97, 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]

(197−100, 197, 144)-Net over F₄ — Digital

Digital (97, 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]

(197−100, 197, 1489)-Net in Base 4 — Upper bound on s

There is no (97, 197, 1490)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41513 301000 628315 350620 922226 348143 060191 166482 718524 985403 020789 319498 294902 655835 992448 535465 875337 142576 669948 613776 > 4¹⁹⁷ [i]