MinT - Best Known (145, 145+47, s)-Nets in Base 4

Best Known (145, 145+47, s)-Nets in Base 4

(145, 145+47, 1032)-Net over F₄ — Constructive and digital

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]

(145, 145+47, 1977)-Net over F₄ — Digital

Digital (145, 192, 1977)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+47, 314068)-Net in Base 4 — Upper bound on s

There is no (145, 192, 314069)-net in base 4, because

1 times m-reduction [i] would yield (145, 191, 314069)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 850646 414887 908971 487049 970593 845618 282761 846393 594329 263399 412183 365521 463465 969406 740872 262585 732962 314733 123968 > 4¹⁹¹ [i]