MinT - Best Known (197−53, 197, s)-Nets in Base 4

Best Known (197−53, 197, s)-Nets in Base 4

(197−53, 197, 531)-Net over F₄ — Constructive and digital

Digital (144, 197, 531)-net over F₄, using

t-expansion [i] based on digital (143, 197, 531)-net over F₄, using
- 7 times m-reduction [i] based on digital (143, 204, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 68, 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]

(197−53, 197, 1313)-Net over F₄ — Digital

Digital (144, 197, 1313)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−53, 197, 121535)-Net in Base 4 — Upper bound on s

There is no (144, 197, 121536)-net in base 4, because

1 times m-reduction [i] would yield (144, 196, 121536)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10088 538378 301056 035126 770335 323467 224969 359127 704316 493622 439135 472455 726692 592911 555451 617254 173812 191143 679709 958373 > 4¹⁹⁶ [i]