MinT - Best Known (206−65, 206, s)-Nets in Base 4

Best Known (206−65, 206, s)-Nets in Base 4

(206−65, 206, 312)-Net over F₄ — Constructive and digital

Digital (141, 206, 312)-net over F₄, using

1 times m-reduction [i] based on digital (141, 207, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 69, 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]

(206−65, 206, 694)-Net over F₄ — Digital

Digital (141, 206, 694)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−65, 206, 30643)-Net in Base 4 — Upper bound on s

There is no (141, 206, 30644)-net in base 4, because

1 times m-reduction [i] would yield (141, 205, 30644)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2646 189071 993125 262730 849664 442940 437255 868591 424279 690968 833431 450367 270883 894069 711076 846211 113982 348170 938016 821060 464155 > 4²⁰⁵ [i]