MinT - Best Known (217−61, 217, s)-Nets in Base 4

Best Known (217−61, 217, s)-Nets in Base 4

(217−61, 217, 531)-Net over F₄ — Constructive and digital

Digital (156, 217, 531)-net over F₄, using

t-expansion [i] based on digital (155, 217, 531)-net over F₄, using
- 5 times m-reduction [i] based on digital (155, 222, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 74, 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]

(217−61, 217, 1174)-Net over F₄ — Digital

Digital (156, 217, 1174)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−61, 217, 86771)-Net in Base 4 — Upper bound on s

There is no (156, 217, 86772)-net in base 4, because

1 times m-reduction [i] would yield (156, 216, 86772)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11092 860616 907094 930592 459886 715675 284940 626596 079446 746303 579352 093471 468402 029848 802454 546291 186613 757561 238905 996840 299346 166744 > 4²¹⁶ [i]