MinT - Best Known (52, 52+45, s)-Nets in Base 7

Best Known (52, 52+45, s)-Nets in Base 7

(52, 52+45, 106)-Net over F₇ — Constructive and digital

Digital (52, 97, 106)-net over F₇, using

1 times m-reduction [i] based on digital (52, 98, 106)-net over F₇, using
- trace code for nets [i] based on digital (3, 49, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(52, 52+45, 198)-Net over F₇ — Digital

Digital (52, 97, 198)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+45, 7337)-Net in Base 7 — Upper bound on s

There is no (52, 97, 7338)-net in base 7, because

1 times m-reduction [i] would yield (52, 96, 7338)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1347 990981 927817 003228 310197 211103 322641 037650 511778 514890 420252 877726 185042 307037 > 7⁹⁶ [i]