MinT - Best Known (240−72, 240, s)-Nets in Base 4

Best Known (240−72, 240, s)-Nets in Base 4

(240−72, 240, 531)-Net over F₄ — Constructive and digital

Digital (168, 240, 531)-net over F₄, using

t-expansion [i] based on digital (167, 240, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 80, 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]

(240−72, 240, 970)-Net over F₄ — Digital

Digital (168, 240, 970)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−72, 240, 49100)-Net in Base 4 — Upper bound on s

There is no (168, 240, 49101)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 122270 178547 814968 219909 230874 422444 919105 055947 545026 510270 712489 151388 688533 790979 859176 162191 146234 726515 880112 587690 272219 129879 108147 573294 > 4²⁴⁰ [i]