MinT - Best Known (218−61, 218, s)-Nets in Base 4

Best Known (218−61, 218, s)-Nets in Base 4

(218−61, 218, 531)-Net over F₄ — Constructive and digital

Digital (157, 218, 531)-net over F₄, using

7 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]

(218−61, 218, 1203)-Net over F₄ — Digital

Digital (157, 218, 1203)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−61, 218, 90876)-Net in Base 4 — Upper bound on s

There is no (157, 218, 90877)-net in base 4, because

1 times m-reduction [i] would yield (157, 217, 90877)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44371 968393 779267 125026 303567 373910 116631 774663 669469 764255 447371 875641 855693 543550 614363 864360 223465 031712 137376 592181 527229 255456 > 4²¹⁷ [i]