MinT - Best Known (250−60, 250, s)-Nets in Base 4

Best Known (250−60, 250, s)-Nets in Base 4

(250−60, 250, 1036)-Net over F₄ — Constructive and digital

Digital (190, 250, 1036)-net over F₄, using

4² times duplication [i] based on digital (188, 248, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 62, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(250−60, 250, 2735)-Net over F₄ — Digital

Digital (190, 250, 2735)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−60, 250, 417646)-Net in Base 4 — Upper bound on s

There is no (190, 250, 417647)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 273578 874666 474795 138303 734907 278779 039168 566249 875191 631267 385972 517867 781675 383249 206486 056574 766127 305817 606680 376684 789079 048011 138003 322625 339774 > 4²⁵⁰ [i]