MinT - Best Known (42, 42+37, s)-Nets in Base 7

Best Known (42, 42+37, s)-Nets in Base 7

(42, 42+37, 104)-Net over F₇ — Constructive and digital

Digital (42, 79, 104)-net over F₇, using

1 times m-reduction [i] based on digital (42, 80, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 40, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(42, 42+37, 162)-Net over F₇ — Digital

Digital (42, 79, 162)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+37, 5770)-Net in Base 7 — Upper bound on s

There is no (42, 79, 5771)-net in base 7, because

1 times m-reduction [i] would yield (42, 78, 5771)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 828806 101242 691514 217542 348074 585703 298989 296723 693673 771435 340013 > 7⁷⁸ [i]