MinT - Best Known (101, 225, s)-Nets in Base 4

Best Known (101, 225, s)-Nets in Base 4

(101, 225, 104)-Net over F₄ — Constructive and digital

Digital (101, 225, 104)-net over F₄, using

t-expansion [i] based on digital (73, 225, 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]

(101, 225, 144)-Net over F₄ — Digital

Digital (101, 225, 144)-net over F₄, using

t-expansion [i] based on digital (91, 225, 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]

(101, 225, 1170)-Net in Base 4 — Upper bound on s

There is no (101, 225, 1171)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2937 998523 726446 219253 975018 639386 051540 938322 512197 771009 631275 428459 853162 294553 296006 542597 723317 159086 621206 524213 295011 995423 359200 > 4²²⁵ [i]