MinT - Best Known (58, 58+35, s)-Nets in Base 7

Best Known (58, 58+35, s)-Nets in Base 7

(58, 58+35, 122)-Net over F₇ — Constructive and digital

Digital (58, 93, 122)-net over F₇, using

1 times m-reduction [i] based on digital (58, 94, 122)-net over F₇, using
- trace code for nets [i] based on digital (11, 47, 61)-net over F₄₉, using
  - net from sequence [i] based on digital (11, 60)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(58, 58+35, 479)-Net over F₇ — Digital

Digital (58, 93, 479)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+35, 44787)-Net in Base 7 — Upper bound on s

There is no (58, 93, 44788)-net in base 7, because

1 times m-reduction [i] would yield (58, 92, 44788)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 561095 220889 780907 769554 215875 093419 148282 407228 534771 625421 563349 502138 280889 > 7⁹² [i]