MinT - Best Known (251−176, 251, s)-Nets in Base 4

Best Known (251−176, 251, s)-Nets in Base 4

(251−176, 251, 104)-Net over F₄ — Constructive and digital

Digital (75, 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]

(251−176, 251, 112)-Net over F₄ — Digital

Digital (75, 251, 112)-net over F₄, using

t-expansion [i] based on digital (73, 251, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(251−176, 251, 513)-Net in Base 4 — Upper bound on s

There is no (75, 251, 514)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 648970 875200 584361 022124 228000 123624 303658 336420 240466 028395 261446 035067 037340 135055 910204 156092 828547 642423 359489 189743 941741 700672 525489 459077 850944 > 4²⁵¹ [i]