MinT - Best Known (192−46, 192, s)-Nets in Base 4

Best Known (192−46, 192, s)-Nets in Base 4

(192−46, 192, 1036)-Net over F₄ — Constructive and digital

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]

(192−46, 192, 2199)-Net over F₄ — Digital

Digital (146, 192, 2199)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−46, 192, 333582)-Net in Base 4 — Upper bound on s

There is no (146, 192, 333583)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 39 404270 076900 499773 240848 416767 527320 961435 026038 568932 141861 960737 516413 435907 911352 251247 829057 025543 933220 169280 > 4¹⁹² [i]