MinT - Best Known (103−24, 103, s)-Nets in Base 4

Best Known (103−24, 103, s)-Nets in Base 4

(103−24, 103, 1032)-Net over F₄ — Constructive and digital

Digital (79, 103, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (79, 104, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 26, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(103−24, 103, 1573)-Net over F₄ — Digital

Digital (79, 103, 1573)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−24, 103, 259361)-Net in Base 4 — Upper bound on s

There is no (79, 103, 259362)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 102 845462 061953 915454 856185 799932 497819 292930 416278 398798 517480 > 4¹⁰³ [i]