MinT - Best Known (231−65, 231, s)-Nets in Base 4

Best Known (231−65, 231, s)-Nets in Base 4

(231−65, 231, 531)-Net over F₄ — Constructive and digital

Digital (166, 231, 531)-net over F₄, using

t-expansion [i] based on digital (165, 231, 531)-net over F₄, using
- 6 times m-reduction [i] based on digital (165, 237, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 79, 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]

(231−65, 231, 1232)-Net over F₄ — Digital

Digital (166, 231, 1232)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−65, 231, 90560)-Net in Base 4 — Upper bound on s

There is no (166, 231, 90561)-net in base 4, because

1 times m-reduction [i] would yield (166, 230, 90561)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 977430 266011 241216 188197 234411 560293 707604 893260 856310 231842 209011 536719 494501 877044 814723 477382 764368 876253 002461 022253 341467 287371 180730 > 4²³⁰ [i]