MinT - Best Known (169, 213, s)-Nets in Base 4

Best Known (169, 213, s)-Nets in Base 4

(169, 213, 1064)-Net over F₄ — Constructive and digital

Digital (169, 213, 1064)-net over F₄, using

4¹ times duplication [i] based on digital (168, 212, 1064)-net over F₄, using
- trace code for nets [i] based on digital (9, 53, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(169, 213, 5424)-Net over F₄ — Digital

Digital (169, 213, 5424)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 213, 2035932)-Net in Base 4 — Upper bound on s

There is no (169, 213, 2035933)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 173 293112 105949 147324 957589 125146 249745 039008 364666 357655 112879 307409 579974 984266 564958 932042 484741 556080 708776 876667 145889 613412 > 4²¹³ [i]