MinT - Best Known (60, 60+39, s)-Nets in Base 7

Best Known (60, 60+39, s)-Nets in Base 7

(60, 60+39, 120)-Net over F₇ — Constructive and digital

Digital (60, 99, 120)-net over F₇, using

1 times m-reduction [i] based on digital (60, 100, 120)-net over F₇, using
- trace code for nets [i] based on digital (10, 50, 60)-net over F₄₉, using
  - net from sequence [i] based on digital (10, 59)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(60, 60+39, 403)-Net over F₇ — Digital

Digital (60, 99, 403)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+39, 30186)-Net in Base 7 — Upper bound on s

There is no (60, 99, 30187)-net in base 7, because

1 times m-reduction [i] would yield (60, 98, 30187)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 66021 124874 596612 271508 277258 054038 474499 918747 004315 344804 769112 461609 838529 381519 > 7⁹⁸ [i]