MinT - Best Known (243−72, 243, s)-Nets in Base 4

Best Known (243−72, 243, s)-Nets in Base 4

(243−72, 243, 531)-Net over F₄ — Constructive and digital

Digital (171, 243, 531)-net over F₄, using

3 times m-reduction [i] based on digital (171, 246, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 82, 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]

(243−72, 243, 1032)-Net over F₄ — Digital

Digital (171, 243, 1032)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−72, 243, 55117)-Net in Base 4 — Upper bound on s

There is no (171, 243, 55118)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 199 874854 927403 308593 795394 918888 534989 973693 482666 709559 929809 987420 694302 939095 513944 696215 168616 726025 438702 880035 642313 519936 090783 180452 712130 > 4²⁴³ [i]