MinT - Best Known (194−40, 194, s)-Nets in Base 4

Best Known (194−40, 194, s)-Nets in Base 4

(194−40, 194, 1060)-Net over F₄ — Constructive and digital

Digital (154, 194, 1060)-net over F₄, using

4² times duplication [i] based on digital (152, 192, 1060)-net over F₄, using
- trace code for nets [i] based on digital (8, 48, 265)-net over F₂₅₆, using
  - net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(194−40, 194, 5091)-Net over F₄ — Digital

Digital (154, 194, 5091)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−40, 194, 1914975)-Net in Base 4 — Upper bound on s

There is no (154, 194, 1914976)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 630 435286 803731 798051 992352 210252 222610 321479 038526 452842 457296 992186 843989 109625 023737 028053 879940 330465 694397 345471 > 4¹⁹⁴ [i]