MinT - Best Known (172−42, 172, s)-Nets in Base 4

Best Known (172−42, 172, s)-Nets in Base 4

(172−42, 172, 1032)-Net over F₄ — Constructive and digital

Digital (130, 172, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 43, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(172−42, 172, 1825)-Net over F₄ — Digital

Digital (130, 172, 1825)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−42, 172, 246887)-Net in Base 4 — Upper bound on s

There is no (130, 172, 246888)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 836864 232934 088425 115388 395931 683580 969621 813517 168884 834946 293301 580343 375373 243046 653947 516206 707790 > 4¹⁷² [i]