MinT - Best Known (199−46, 199, s)-Nets in Base 4

Best Known (199−46, 199, s)-Nets in Base 4

(199−46, 199, 1040)-Net over F₄ — Constructive and digital

Digital (153, 199, 1040)-net over F₄, using

1 times m-reduction [i] based on digital (153, 200, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 50, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(199−46, 199, 2723)-Net over F₄ — Digital

Digital (153, 199, 2723)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−46, 199, 508682)-Net in Base 4 — Upper bound on s

There is no (153, 199, 508683)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 645575 613825 379489 944626 544690 084438 259889 346469 627121 362864 447698 368400 653273 600056 674080 664542 230193 370771 738827 438080 > 4¹⁹⁹ [i]