MinT - Best Known (172−39, 172, s)-Nets in Base 4

Best Known (172−39, 172, s)-Nets in Base 4

(172−39, 172, 1044)-Net over F₄ — Constructive and digital

Digital (133, 172, 1044)-net over F₄, using

trace code for nets [i] based on digital (4, 43, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(172−39, 172, 2678)-Net over F₄ — Digital

Digital (133, 172, 2678)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−39, 172, 692826)-Net in Base 4 — Upper bound on s

There is no (133, 172, 692827)-net in base 4, because

1 times m-reduction [i] would yield (133, 171, 692827)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 959073 795717 183785 450348 367112 970312 611195 872711 592815 727114 209377 923301 925697 874127 939555 925382 412236 > 4¹⁷¹ [i]