MinT - Best Known (197−98, 197, s)-Nets in Base 4

Best Known (197−98, 197, s)-Nets in Base 4

(197−98, 197, 104)-Net over F₄ — Constructive and digital

Digital (99, 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]

(197−98, 197, 144)-Net over F₄ — Digital

Digital (99, 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]

(197−98, 197, 1637)-Net in Base 4 — Upper bound on s

There is no (99, 197, 1638)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40665 284194 554209 116646 019743 264329 313865 684065 279357 203400 381179 131055 026269 979705 129401 160783 544437 014225 833613 963524 > 4¹⁹⁷ [i]