MinT - Best Known (139, 139+44, s)-Nets in Base 4

Best Known (139, 139+44, s)-Nets in Base 4

(139, 139+44, 1032)-Net over F₄ — Constructive and digital

Digital (139, 183, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (139, 184, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 46, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(139, 139+44, 2075)-Net over F₄ — Digital

Digital (139, 183, 2075)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+44, 307433)-Net in Base 4 — Upper bound on s

There is no (139, 183, 307434)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150 313128 799973 954302 371144 635358 600809 855967 223562 236721 474103 315869 724238 782995 054817 231227 916445 360316 480680 > 4¹⁸³ [i]