MinT - Best Known (195−47, 195, s)-Nets in Base 4

Best Known (195−47, 195, s)-Nets in Base 4

(195−47, 195, 1032)-Net over F₄ — Constructive and digital

Digital (148, 195, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (148, 196, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 49, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(195−47, 195, 2162)-Net over F₄ — Digital

Digital (148, 195, 2162)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−47, 195, 376321)-Net in Base 4 — Upper bound on s

There is no (148, 195, 376322)-net in base 4, because

1 times m-reduction [i] would yield (148, 194, 376322)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 630 464835 206207 470075 728319 450168 414807 976964 014218 839736 629232 562023 186013 878129 029459 499674 273994 897302 678853 458688 > 4¹⁹⁴ [i]