MinT - Best Known (119−27, 119, s)-Nets in Base 4

Best Known (119−27, 119, s)-Nets in Base 4

(119−27, 119, 1036)-Net over F₄ — Constructive and digital

Digital (92, 119, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (92, 120, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 30, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(119−27, 119, 2016)-Net over F₄ — Digital

Digital (92, 119, 2016)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−27, 119, 550971)-Net in Base 4 — Upper bound on s

There is no (92, 119, 550972)-net in base 4, because

1 times m-reduction [i] would yield (92, 118, 550972)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 110429 664988 582725 010108 010461 556189 036178 536796 853911 565400 044951 854748 > 4¹¹⁸ [i]