MinT - Best Known (159, 159+41, s)-Nets in Base 4

Best Known (159, 159+41, s)-Nets in Base 4

(159, 159+41, 1064)-Net over F₄ — Constructive and digital

Digital (159, 200, 1064)-net over F₄, using

trace code for nets [i] based on digital (9, 50, 266)-net over F₂₅₆, using
- net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(159, 159+41, 5402)-Net over F₄ — Digital

Digital (159, 200, 5402)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+41, 2708191)-Net in Base 4 — Upper bound on s

There is no (159, 200, 2708192)-net in base 4, because

1 times m-reduction [i] would yield (159, 199, 2708192)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 645567 034092 274060 152632 835891 558885 009348 110489 564010 670148 408023 659438 025312 361998 781650 198623 418524 765137 305926 628519 > 4¹⁹⁹ [i]