MinT - Best Known (93−33, 93, s)-Nets in Base 7

Best Known (93−33, 93, s)-Nets in Base 7

(93−33, 93, 126)-Net over F₇ — Constructive and digital

Digital (60, 93, 126)-net over F₇, using

1 times m-reduction [i] based on digital (60, 94, 126)-net over F₇, using
- trace code for nets [i] based on digital (13, 47, 63)-net over F₄₉, using
  - net from sequence [i] based on digital (13, 62)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(93−33, 93, 625)-Net over F₇ — Digital

Digital (60, 93, 625)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−33, 93, 81968)-Net in Base 7 — Upper bound on s

There is no (60, 93, 81969)-net in base 7, because

1 times m-reduction [i] would yield (60, 92, 81969)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 561120 798245 936401 260822 098893 237939 747881 065837 053580 928964 746191 352233 979265 > 7⁹² [i]