MinT - Best Known (49, 49+44, s)-Nets in Base 7

Best Known (49, 49+44, s)-Nets in Base 7

(49, 49+44, 104)-Net over F₇ — Constructive and digital

Digital (49, 93, 104)-net over F₇, using

1 times m-reduction [i] based on digital (49, 94, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 47, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(49, 49+44, 177)-Net over F₇ — Digital

Digital (49, 93, 177)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+44, 5624)-Net in Base 7 — Upper bound on s

There is no (49, 93, 5625)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 937946 981932 229742 447155 168621 720685 457965 201405 261170 739830 460718 958057 712001 > 7⁹³ [i]