MinT - Best Known (216−62, 216, s)-Nets in Base 4

Best Known (216−62, 216, s)-Nets in Base 4

(216−62, 216, 531)-Net over F₄ — Constructive and digital

Digital (154, 216, 531)-net over F₄, using

t-expansion [i] based on digital (153, 216, 531)-net over F₄, using
- 3 times m-reduction [i] based on digital (153, 219, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 73, 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]

(216−62, 216, 1067)-Net over F₄ — Digital

Digital (154, 216, 1067)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−62, 216, 64824)-Net in Base 4 — Upper bound on s

There is no (154, 216, 64825)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11092 129525 452091 012529 488072 319467 050022 033185 933329 300518 355616 196183 379001 563462 015656 127551 851732 637297 925494 940069 362829 613280 > 4²¹⁶ [i]