MinT - Best Known (217−59, 217, s)-Nets in Base 4

Best Known (217−59, 217, s)-Nets in Base 4

(217−59, 217, 531)-Net over F₄ — Constructive and digital

Digital (158, 217, 531)-net over F₄, using

t-expansion [i] based on digital (157, 217, 531)-net over F₄, using
- 8 times m-reduction [i] based on digital (157, 225, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 75, 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]

(217−59, 217, 1365)-Net over F₄ — Digital

Digital (158, 217, 1365)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−59, 217, 118637)-Net in Base 4 — Upper bound on s

There is no (158, 217, 118638)-net in base 4, because

1 times m-reduction [i] would yield (158, 216, 118638)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11091 243712 277377 826631 956634 107552 686465 555270 467569 271349 241075 476470 952225 130601 807283 328488 852477 990698 259339 670657 304195 604594 > 4²¹⁶ [i]