MinT - Best Known (152, 152+59, s)-Nets in Base 4

Best Known (152, 152+59, s)-Nets in Base 4

(152, 152+59, 531)-Net over F₄ — Constructive and digital

Digital (152, 211, 531)-net over F₄, using

t-expansion [i] based on digital (151, 211, 531)-net over F₄, using
- 5 times m-reduction [i] based on digital (151, 216, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 72, 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]

(152, 152+59, 1174)-Net over F₄ — Digital

Digital (152, 211, 1174)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 152+59, 89049)-Net in Base 4 — Upper bound on s

There is no (152, 211, 89050)-net in base 4, because

1 times m-reduction [i] would yield (152, 210, 89050)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 708368 784094 227373 238494 415358 132910 367827 710910 061528 594637 106055 637260 039307 677883 046715 245120 142031 490789 201785 330296 387792 > 4²¹⁰ [i]