MinT - Best Known (55−23, 55, s)-Nets in Base 7

Best Known (55−23, 55, s)-Nets in Base 7

(55−23, 55, 108)-Net over F₇ — Constructive and digital

Digital (32, 55, 108)-net over F₇, using

1 times m-reduction [i] based on digital (32, 56, 108)-net over F₇, using
- trace code for nets [i] based on digital (4, 28, 54)-net over F₄₉, using
  - net from sequence [i] based on digital (4, 53)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(55−23, 55, 205)-Net over F₇ — Digital

Digital (32, 55, 205)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−23, 55, 11515)-Net in Base 7 — Upper bound on s

There is no (32, 55, 11516)-net in base 7, because

1 times m-reduction [i] would yield (32, 54, 11516)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 4321 749144 627539 681504 741713 423991 588365 100833 > 7⁵⁴ [i]