MinT - Best Known (193−46, 193, s)-Nets in Base 4

Best Known (193−46, 193, s)-Nets in Base 4

(193−46, 193, 1036)-Net over F₄ — Constructive and digital

Digital (147, 193, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (146, 192, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 48, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(193−46, 193, 2267)-Net over F₄ — Digital

Digital (147, 193, 2267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−46, 193, 354307)-Net in Base 4 — Upper bound on s

There is no (147, 193, 354308)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 157 609614 793032 125368 189025 657123 247629 157861 440994 646195 625692 801706 770779 386763 352564 020532 403793 217711 121242 478080 > 4¹⁹³ [i]