MinT - Best Known (58, 58+43, s)-Nets in Base 7

Best Known (58, 58+43, s)-Nets in Base 7

(58, 58+43, 114)-Net over F₇ — Constructive and digital

Digital (58, 101, 114)-net over F₇, using

1 times m-reduction [i] based on digital (58, 102, 114)-net over F₇, using
- trace code for nets [i] based on digital (7, 51, 57)-net over F₄₉, using
  - net from sequence [i] based on digital (7, 56)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(58, 58+43, 289)-Net over F₇ — Digital

Digital (58, 101, 289)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+43, 15283)-Net in Base 7 — Upper bound on s

There is no (58, 101, 15284)-net in base 7, because

1 times m-reduction [i] would yield (58, 100, 15284)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 234891 663044 625098 822739 988401 536053 086418 156896 441533 945630 135247 903225 266268 006745 > 7¹⁰⁰ [i]