MinT - Best Known (40, 71, s)-Nets in Base 7

Best Known (40, 71, s)-Nets in Base 7

(40, 71, 108)-Net over F₇ — Constructive and digital

Digital (40, 71, 108)-net over F₇, using

1 times m-reduction [i] based on digital (40, 72, 108)-net over F₇, using
- trace code for nets [i] based on digital (4, 36, 54)-net over F₄₉, using
  - net from sequence [i] based on digital (4, 53)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(40, 71, 199)-Net over F₇ — Digital

Digital (40, 71, 199)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 71, 9396)-Net in Base 7 — Upper bound on s

There is no (40, 71, 9397)-net in base 7, because

1 times m-reduction [i] would yield (40, 70, 9397)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 143611 048407 282098 195402 838275 882569 524579 028089 654119 516311 > 7⁷⁰ [i]