MinT - Best Known (191−56, 191, s)-Nets in Base 4

Best Known (191−56, 191, s)-Nets in Base 4

(191−56, 191, 531)-Net over F₄ — Constructive and digital

Digital (135, 191, 531)-net over F₄, using

1 times m-reduction [i] based on digital (135, 192, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 64, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(191−56, 191, 879)-Net over F₄ — Digital

Digital (135, 191, 879)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−56, 191, 48148)-Net in Base 4 — Upper bound on s

There is no (135, 191, 48149)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 850588 143683 231332 684240 447273 518113 272048 283694 506432 325328 609304 745726 684579 540735 310324 873036 409963 734223 928448 > 4¹⁹¹ [i]