MinT - Best Known (215−65, 215, s)-Nets in Base 4

Best Known (215−65, 215, s)-Nets in Base 4

(215−65, 215, 450)-Net over F₄ — Constructive and digital

Digital (150, 215, 450)-net over F₄, using

5 times m-reduction [i] based on digital (150, 220, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 110, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(215−65, 215, 855)-Net over F₄ — Digital

Digital (150, 215, 855)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−65, 215, 45267)-Net in Base 4 — Upper bound on s

There is no (150, 215, 45268)-net in base 4, because

1 times m-reduction [i] would yield (150, 214, 45268)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 693 520629 831939 703787 574452 218198 051707 856436 885398 955506 411049 690128 336171 502132 811320 202379 686922 037680 221632 490431 325328 226566 > 4²¹⁴ [i]