MinT - Best Known (154, 154+61, s)-Nets in Base 4

Best Known (154, 154+61, s)-Nets in Base 4

(154, 154+61, 531)-Net over F₄ — Constructive and digital

Digital (154, 215, 531)-net over F₄, using

t-expansion [i] based on digital (153, 215, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (153, 219, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 73, 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]

(154, 154+61, 1118)-Net over F₄ — Digital

Digital (154, 215, 1118)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+61, 79109)-Net in Base 4 — Upper bound on s

There is no (154, 215, 79110)-net in base 4, because

1 times m-reduction [i] would yield (154, 214, 79110)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 693 350713 620127 749228 334870 075442 525410 604959 837975 699641 883106 446053 634379 851284 777043 548688 729340 304546 495170 202477 371660 904832 > 4²¹⁴ [i]