MinT - Best Known (46, 46+21, s)-Nets in Base 7

Best Known (46, 46+21, s)-Nets in Base 7

(46, 46+21, 204)-Net over F₇ — Constructive and digital

Digital (46, 67, 204)-net over F₇, using

7¹ times duplication [i] based on digital (45, 66, 204)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (12, 22, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 11, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. digital (23, 44, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 22, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(46, 46+21, 948)-Net over F₇ — Digital

Digital (46, 67, 948)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+21, 285405)-Net in Base 7 — Upper bound on s

There is no (46, 67, 285406)-net in base 7, because

1 times m-reduction [i] would yield (46, 66, 285406)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 59 768766 750700 832723 198231 918017 345412 506733 605200 422173 > 7⁶⁶ [i]