MinT - Best Known (228−67, 228, s)-Nets in Base 4

Best Known (228−67, 228, s)-Nets in Base 4

(228−67, 228, 531)-Net over F₄ — Constructive and digital

Digital (161, 228, 531)-net over F₄, using

3 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]

(228−67, 228, 1011)-Net over F₄ — Digital

Digital (161, 228, 1011)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−67, 228, 60741)-Net in Base 4 — Upper bound on s

There is no (161, 228, 60742)-net in base 4, because

1 times m-reduction [i] would yield (161, 227, 60742)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46539 701613 140288 273382 841252 820804 692776 360978 391773 519763 787525 659982 026010 191564 707384 974920 732206 096062 061381 905280 234702 375359 323114 > 4²²⁷ [i]