MinT - Best Known (164, 164+52, s)-Nets in Base 4

Best Known (164, 164+52, s)-Nets in Base 4

(164, 164+52, 1036)-Net over F₄ — Constructive and digital

Digital (164, 216, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 54, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(164, 164+52, 2373)-Net over F₄ — Digital

Digital (164, 216, 2373)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+52, 353081)-Net in Base 4 — Upper bound on s

There is no (164, 216, 353082)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11091 122502 571678 311464 944723 798478 104537 374607 288942 533389 181254 069718 206417 074434 814218 753544 170891 063981 978978 523032 995885 939656 > 4²¹⁶ [i]