MinT - Best Known (194−56, 194, s)-Nets in Base 4

Best Known (194−56, 194, s)-Nets in Base 4

(194−56, 194, 531)-Net over F₄ — Constructive and digital

Digital (138, 194, 531)-net over F₄, using

t-expansion [i] based on digital (137, 194, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (137, 195, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 65, 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]

(194−56, 194, 952)-Net over F₄ — Digital

Digital (138, 194, 952)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−56, 194, 55862)-Net in Base 4 — Upper bound on s

There is no (138, 194, 55863)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 630 524553 717194 267999 222564 619967 127230 414040 215371 199242 375037 295293 117751 494305 534516 666433 952201 809747 477279 478860 > 4¹⁹⁴ [i]