MinT - Best Known (180, 180+77, s)-Nets in Base 4

Best Known (180, 180+77, s)-Nets in Base 4

(180, 180+77, 531)-Net over F₄ — Constructive and digital

Digital (180, 257, 531)-net over F₄, using

t-expansion [i] based on digital (179, 257, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 86, 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]

(180, 180+77, 1035)-Net over F₄ — Digital

Digital (180, 257, 1035)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+77, 56941)-Net in Base 4 — Upper bound on s

There is no (180, 257, 56942)-net in base 4, because

1 times m-reduction [i] would yield (180, 256, 56942)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13414 020213 330070 162329 724720 204564 277114 829691 244727 122516 522670 198210 544699 258286 454699 081586 028934 549952 055436 844878 990176 853469 815107 703339 698269 495540 > 4²⁵⁶ [i]