MinT - Best Known (172, 172+56, s)-Nets in Base 4

Best Known (172, 172+56, s)-Nets in Base 4

(172, 172+56, 1032)-Net over F₄ — Constructive and digital

Digital (172, 228, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 57, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(172, 172+56, 2255)-Net over F₄ — Digital

Digital (172, 228, 2255)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+56, 300842)-Net in Base 4 — Upper bound on s

There is no (172, 228, 300843)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186077 853106 290258 375108 393224 202109 579741 478496 565389 033081 096711 526717 237608 390251 008237 040511 618529 935694 088015 510078 121541 675529 409880 > 4²²⁸ [i]