MinT - Best Known (221−52, 221, s)-Nets in Base 4

Best Known (221−52, 221, s)-Nets in Base 4

(221−52, 221, 1040)-Net over F₄ — Constructive and digital

Digital (169, 221, 1040)-net over F₄, using

4¹ times duplication [i] based on digital (168, 220, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 55, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(221−52, 221, 2715)-Net over F₄ — Digital

Digital (169, 221, 2715)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−52, 221, 460958)-Net in Base 4 — Upper bound on s

There is no (169, 221, 460959)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 357214 862007 566261 176375 176167 097766 251232 076787 843060 903122 960423 156197 342926 590916 877208 081436 545797 926095 233253 907674 962706 733629 > 4²²¹ [i]