MinT - Best Known (97, 251, s)-Nets in Base 4

Best Known (97, 251, s)-Nets in Base 4

(97, 251, 104)-Net over F₄ — Constructive and digital

Digital (97, 251, 104)-net over F₄, using

t-expansion [i] based on digital (73, 251, 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]

(97, 251, 144)-Net over F₄ — Digital

Digital (97, 251, 144)-net over F₄, using

t-expansion [i] based on digital (91, 251, 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]

(97, 251, 839)-Net in Base 4 — Upper bound on s

There is no (97, 251, 840)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 422212 878360 124925 933339 163081 382251 277036 560794 322738 870012 402051 283241 855828 797481 352608 674566 703602 707095 576642 076171 595990 827902 091723 971304 181792 > 4²⁵¹ [i]