MinT - Best Known (249−152, 249, s)-Nets in Base 4

Best Known (249−152, 249, s)-Nets in Base 4

(249−152, 249, 104)-Net over F₄ — Constructive and digital

Digital (97, 249, 104)-net over F₄, using

t-expansion [i] based on digital (73, 249, 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]

(249−152, 249, 144)-Net over F₄ — Digital

Digital (97, 249, 144)-net over F₄, using

t-expansion [i] based on digital (91, 249, 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]

(249−152, 249, 849)-Net in Base 4 — Upper bound on s

There is no (97, 249, 850)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 827579 775192 201367 382951 873158 200212 184430 680320 731090 591691 864426 643092 510431 707574 615681 115461 101278 114879 690849 458095 860562 765872 627480 460824 403532 > 4²⁴⁹ [i]