MinT - Best Known (144, 144+36, s)-Nets in Base 4

Best Known (144, 144+36, s)-Nets in Base 4

(144, 144+36, 1064)-Net over F₄ — Constructive and digital

Digital (144, 180, 1064)-net over F₄, using

trace code for nets [i] based on digital (9, 45, 266)-net over F₂₅₆, using
- net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(144, 144+36, 5804)-Net over F₄ — Digital

Digital (144, 180, 5804)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+36, 2640014)-Net in Base 4 — Upper bound on s

There is no (144, 180, 2640015)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 348548 861956 266109 503057 163526 132290 074260 650654 487318 728312 225992 436051 327702 167668 162673 042230 555842 198040 > 4¹⁸⁰ [i]