MinT - Best Known (136, 180, s)-Nets in Base 4

Best Known (136, 180, s)-Nets in Base 4

(136, 180, 1032)-Net over F₄ — Constructive and digital

Digital (136, 180, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 45, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(136, 180, 1886)-Net over F₄ — Digital

Digital (136, 180, 1886)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 180, 254475)-Net in Base 4 — Upper bound on s

There is no (136, 180, 254476)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 348555 281693 142166 727624 834072 115614 244999 029797 875542 692040 118687 821161 142373 244639 225575 304197 859211 779136 > 4¹⁸⁰ [i]