MinT - Best Known (238−69, 238, s)-Nets in Base 4

Best Known (238−69, 238, s)-Nets in Base 4

(238−69, 238, 531)-Net over F₄ — Constructive and digital

Digital (169, 238, 531)-net over F₄, using

5 times m-reduction [i] based on digital (169, 243, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 81, 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]

(238−69, 238, 1110)-Net over F₄ — Digital

Digital (169, 238, 1110)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−69, 238, 70940)-Net in Base 4 — Upper bound on s

There is no (169, 238, 70941)-net in base 4, because

1 times m-reduction [i] would yield (169, 237, 70941)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48781 800278 931521 771117 717100 466666 312405 360794 450640 666835 033145 614983 154164 672179 963918 207828 126219 523240 034605 266239 576712 140393 477580 273040 > 4²³⁷ [i]