MinT - Best Known (155, 155+63, s)-Nets in Base 4

Best Known (155, 155+63, s)-Nets in Base 4

(155, 155+63, 531)-Net over F₄ — Constructive and digital

Digital (155, 218, 531)-net over F₄, using

4 times m-reduction [i] based on digital (155, 222, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 74, 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]

(155, 155+63, 1045)-Net over F₄ — Digital

Digital (155, 218, 1045)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(155, 155+63, 67790)-Net in Base 4 — Upper bound on s

There is no (155, 218, 67791)-net in base 4, because

1 times m-reduction [i] would yield (155, 217, 67791)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44371 065207 487624 826727 481454 074592 356723 563729 900059 375924 263929 805468 886193 486533 077010 825349 282295 982757 772707 832300 887753 062224 > 4²¹⁷ [i]