MinT - Best Known (194−60, 194, s)-Nets in Base 4

Best Known (194−60, 194, s)-Nets in Base 4

(194−60, 194, 312)-Net over F₄ — Constructive and digital

Digital (134, 194, 312)-net over F₄, using

t-expansion [i] based on digital (133, 194, 312)-net over F₄, using
- 1 times m-reduction [i] based on digital (133, 195, 312)-net over F₄, using
  - trace code for nets [i] based on digital (3, 65, 104)-net over F₆₄, using
    - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(194−60, 194, 714)-Net over F₄ — Digital

Digital (134, 194, 714)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−60, 194, 31379)-Net in Base 4 — Upper bound on s

There is no (134, 194, 31380)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 630 566678 248381 304027 783064 184403 682220 843072 570641 098753 405220 111156 602884 057579 667298 435077 020447 600271 654836 098016 > 4¹⁹⁴ [i]