MinT - Best Known (50, 50+47, s)-Nets in Base 7

Best Known (50, 50+47, s)-Nets in Base 7

(50, 50+47, 102)-Net over F₇ — Constructive and digital

Digital (50, 97, 102)-net over F₇, using

1 times m-reduction [i] based on digital (50, 98, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 49, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(50, 50+47, 167)-Net over F₇ — Digital

Digital (50, 97, 167)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+47, 5277)-Net in Base 7 — Upper bound on s

There is no (50, 97, 5278)-net in base 7, because

1 times m-reduction [i] would yield (50, 96, 5278)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1348 304565 011789 718903 355107 527054 649175 396721 343226 116230 871712 438455 039946 733953 > 7⁹⁶ [i]