MinT - Best Known (228−65, 228, s)-Nets in Base 4

Best Known (228−65, 228, s)-Nets in Base 4

(228−65, 228, 531)-Net over F₄ — Constructive and digital

Digital (163, 228, 531)-net over F₄, using

6 times m-reduction [i] based on digital (163, 234, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 78, 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]

(228−65, 228, 1151)-Net over F₄ — Digital

Digital (163, 228, 1151)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−65, 228, 79520)-Net in Base 4 — Upper bound on s

There is no (163, 228, 79521)-net in base 4, because

1 times m-reduction [i] would yield (163, 227, 79521)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46526 321804 477448 268050 547598 044457 307817 024821 630139 676881 308143 325499 611697 672057 415028 683475 176619 986214 012252 179864 695483 036392 372349 > 4²²⁷ [i]