MinT - Best Known (229−67, 229, s)-Nets in Base 4

Best Known (229−67, 229, s)-Nets in Base 4

(229−67, 229, 531)-Net over F₄ — Constructive and digital

Digital (162, 229, 531)-net over F₄, using

t-expansion [i] based on digital (161, 229, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (161, 231, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 77, 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]

(229−67, 229, 1034)-Net over F₄ — Digital

Digital (162, 229, 1034)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−67, 229, 63348)-Net in Base 4 — Upper bound on s

There is no (162, 229, 63349)-net in base 4, because

1 times m-reduction [i] would yield (162, 228, 63349)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186137 530119 411360 006493 401361 070110 211892 015497 190732 896177 773496 190122 132281 278657 081224 309442 541364 219266 409774 284136 454129 452080 873216 > 4²²⁸ [i]