MinT - Best Known (196−62, 196, s)-Nets in Base 4

Best Known (196−62, 196, s)-Nets in Base 4

(196−62, 196, 312)-Net over F₄ — Constructive and digital

Digital (134, 196, 312)-net over F₄, using

4¹ times duplication [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]

(196−62, 196, 659)-Net over F₄ — Digital

Digital (134, 196, 659)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−62, 196, 26489)-Net in Base 4 — Upper bound on s

There is no (134, 196, 26490)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10095 834723 486907 061440 092308 518755 621152 315825 926061 438817 625790 318137 882130 394734 099045 199367 123306 063964 550749 350000 > 4¹⁹⁶ [i]