MinT - Best Known (125, 125+36, s)-Nets in Base 4

Best Known (125, 125+36, s)-Nets in Base 4

(125, 125+36, 1044)-Net over F₄ — Constructive and digital

Digital (125, 161, 1044)-net over F₄, using

4¹ times duplication [i] based on digital (124, 160, 1044)-net over F₄, using
- trace code for nets [i] based on digital (4, 40, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(125, 125+36, 2744)-Net over F₄ — Digital

Digital (125, 161, 2744)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 125+36, 611069)-Net in Base 4 — Upper bound on s

There is no (125, 161, 611070)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 544061 950792 461547 381460 262872 464657 197569 094890 826496 941762 529926 205251 562845 706103 209082 521622 > 4¹⁶¹ [i]