MinT - Best Known (220−50, 220, s)-Nets in Base 4

Best Known (220−50, 220, s)-Nets in Base 4

(220−50, 220, 1048)-Net over F₄ — Constructive and digital

Digital (170, 220, 1048)-net over F₄, using

trace code for nets [i] based on digital (5, 55, 262)-net over F₂₅₆, using
- net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(220−50, 220, 3240)-Net over F₄ — Digital

Digital (170, 220, 3240)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−50, 220, 673937)-Net in Base 4 — Upper bound on s

There is no (170, 220, 673938)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 839303 881047 696420 122350 402706 560676 873750 993883 686702 061088 909893 385117 275179 401160 982131 435688 407616 620734 032783 474134 583502 344560 > 4²²⁰ [i]