MinT - Best Known (252−71, 252, s)-Nets in Base 4

Best Known (252−71, 252, s)-Nets in Base 4

(252−71, 252, 531)-Net over F₄ — Constructive and digital

Digital (181, 252, 531)-net over F₄, using

t-expansion [i] based on digital (179, 252, 531)-net over F₄, using
- 6 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]

(252−71, 252, 1319)-Net over F₄ — Digital

Digital (181, 252, 1319)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−71, 252, 96303)-Net in Base 4 — Upper bound on s

There is no (181, 252, 96304)-net in base 4, because

1 times m-reduction [i] would yield (181, 251, 96304)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 094416 141769 688628 166347 511113 133705 324465 878953 953144 593264 944187 039490 291114 769614 532979 924713 815186 937963 948259 426400 438228 720569 648639 498765 432045 > 4²⁵¹ [i]