MinT - Best Known (164−39, 164, s)-Nets in Base 4

Best Known (164−39, 164, s)-Nets in Base 4

(164−39, 164, 1036)-Net over F₄ — Constructive and digital

Digital (125, 164, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 41, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(164−39, 164, 2005)-Net over F₄ — Digital

Digital (125, 164, 2005)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−39, 164, 386471)-Net in Base 4 — Upper bound on s

There is no (125, 164, 386472)-net in base 4, because

1 times m-reduction [i] would yield (125, 163, 386472)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 136 703378 657407 386643 603934 537561 762307 509003 453573 911528 232980 815047 881977 283902 144992 837992 480654 > 4¹⁶³ [i]