MinT - Best Known (54, 54+43, s)-Nets in Base 7

Best Known (54, 54+43, s)-Nets in Base 7

(54, 54+43, 110)-Net over F₇ — Constructive and digital

Digital (54, 97, 110)-net over F₇, using

1 times m-reduction [i] based on digital (54, 98, 110)-net over F₇, using
- trace code for nets [i] based on digital (5, 49, 55)-net over F₄₉, using
  - net from sequence [i] based on digital (5, 54)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(54, 54+43, 237)-Net over F₇ — Digital

Digital (54, 97, 237)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+43, 10546)-Net in Base 7 — Upper bound on s

There is no (54, 97, 10547)-net in base 7, because

1 times m-reduction [i] would yield (54, 96, 10547)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1349 589247 377418 294810 233074 700931 683211 320263 954400 194831 640908 187167 613275 998843 > 7⁹⁶ [i]