MinT - Best Known (117−35, 117, s)-Nets in Base 4

Best Known (117−35, 117, s)-Nets in Base 4

(117−35, 117, 312)-Net over F₄ — Constructive and digital

Digital (82, 117, 312)-net over F₄, using

t-expansion [i] based on digital (81, 117, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 39, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(117−35, 117, 549)-Net over F₄ — Digital

Digital (82, 117, 549)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−35, 117, 30676)-Net in Base 4 — Upper bound on s

There is no (82, 117, 30677)-net in base 4, because

1 times m-reduction [i] would yield (82, 116, 30677)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6903 983218 545909 849610 194873 679637 126671 525650 400238 902727 720052 540880 > 4¹¹⁶ [i]