MinT - Best Known (48, 48+45, s)-Nets in Base 7

Best Known (48, 48+45, s)-Nets in Base 7

(48, 48+45, 102)-Net over F₇ — Constructive and digital

Digital (48, 93, 102)-net over F₇, using

1 times m-reduction [i] based on digital (48, 94, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 47, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(48, 48+45, 162)-Net over F₇ — Digital

Digital (48, 93, 162)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 48+45, 5147)-Net in Base 7 — Upper bound on s

There is no (48, 93, 5148)-net in base 7, because

1 times m-reduction [i] would yield (48, 92, 5148)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 563432 780307 133164 592565 684073 135059 560469 505118 240055 729993 601676 556658 397513 > 7⁹² [i]