MinT - Best Known (97−37, 97, s)-Nets in Base 7

Best Known (97−37, 97, s)-Nets in Base 7

(97−37, 97, 122)-Net over F₇ — Constructive and digital

Digital (60, 97, 122)-net over F₇, using

1 times m-reduction [i] based on digital (60, 98, 122)-net over F₇, using
- trace code for nets [i] based on digital (11, 49, 61)-net over F₄₉, using
  - net from sequence [i] based on digital (11, 60)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(97−37, 97, 463)-Net over F₇ — Digital

Digital (60, 97, 463)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−37, 97, 40461)-Net in Base 7 — Upper bound on s

There is no (60, 97, 40462)-net in base 7, because

1 times m-reduction [i] would yield (60, 96, 40462)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1347 271119 675190 251323 554535 971684 113300 045986 779308 869636 219183 172572 861671 037965 > 7⁹⁶ [i]