MinT - Best Known (250−154, 250, s)-Nets in Base 4

Best Known (250−154, 250, s)-Nets in Base 4

(250−154, 250, 104)-Net over F₄ — Constructive and digital

Digital (96, 250, 104)-net over F₄, using

t-expansion [i] based on digital (73, 250, 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]

(250−154, 250, 144)-Net over F₄ — Digital

Digital (96, 250, 144)-net over F₄, using

t-expansion [i] based on digital (91, 250, 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]

(250−154, 250, 823)-Net in Base 4 — Upper bound on s

There is no (96, 250, 824)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 374722 713042 871806 213314 348658 097595 691221 773476 366051 905417 415347 475810 238086 695595 339346 547263 850732 438900 337448 808151 906805 669657 513345 931803 005400 > 4²⁵⁰ [i]