MinT - Best Known (188−38, 188, s)-Nets in Base 4

Best Known (188−38, 188, s)-Nets in Base 4

(188−38, 188, 1064)-Net over F₄ — Constructive and digital

Digital (150, 188, 1064)-net over F₄, using

trace code for nets [i] based on digital (9, 47, 266)-net over F₂₅₆, using
- net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(188−38, 188, 5615)-Net over F₄ — Digital

Digital (150, 188, 5615)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−38, 188, 2395061)-Net in Base 4 — Upper bound on s

There is no (150, 188, 2395062)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 153914 838548 033791 970755 598973 628361 907635 327936 277813 278911 003602 869373 498506 397453 540531 389149 567135 920994 852690 > 4¹⁸⁸ [i]