MinT - Best Known (193−47, 193, s)-Nets in Base 4

Best Known (193−47, 193, s)-Nets in Base 4

(193−47, 193, 1032)-Net over F₄ — Constructive and digital

Digital (146, 193, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (145, 192, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 48, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(193−47, 193, 2037)-Net over F₄ — Digital

Digital (146, 193, 2037)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−47, 193, 333582)-Net in Base 4 — Upper bound on s

There is no (146, 193, 333583)-net in base 4, because

1 times m-reduction [i] would yield (146, 192, 333583)-net in base 4, but
- 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]