MinT - Best Known (107, 139, s)-Nets in Base 4

Best Known (107, 139, s)-Nets in Base 4

(107, 139, 1036)-Net over F₄ — Constructive and digital

Digital (107, 139, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (107, 140, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 35, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(107, 139, 2088)-Net over F₄ — Digital

Digital (107, 139, 2088)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 139, 385300)-Net in Base 4 — Upper bound on s

There is no (107, 139, 385301)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 485684 335222 766315 212957 541848 108222 196901 425105 376980 506046 567691 817902 210767 226781 > 4¹³⁹ [i]