MinT - Best Known (91−43, 91, s)-Nets in Base 7

Best Known (91−43, 91, s)-Nets in Base 7

(91−43, 91, 104)-Net over F₇ — Constructive and digital

Digital (48, 91, 104)-net over F₇, using

1 times m-reduction [i] based on digital (48, 92, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 46, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(91−43, 91, 175)-Net over F₇ — Digital

Digital (48, 91, 175)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(91−43, 91, 6042)-Net in Base 7 — Upper bound on s

There is no (48, 91, 6043)-net in base 7, because

1 times m-reduction [i] would yield (48, 90, 6043)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 11467 633440 829581 237487 759292 542841 211454 791060 249538 737641 577120 958145 472043 > 7⁹⁰ [i]