MinT - Best Known (57, 57+30, s)-Nets in Base 7

Best Known (57, 57+30, s)-Nets in Base 7

(57, 57+30, 126)-Net over F₇ — Constructive and digital

Digital (57, 87, 126)-net over F₇, using

1 times m-reduction [i] based on digital (57, 88, 126)-net over F₇, using
- trace code for nets [i] based on digital (13, 44, 63)-net over F₄₉, using
  - net from sequence [i] based on digital (13, 62)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(57, 57+30, 682)-Net over F₇ — Digital

Digital (57, 87, 682)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+30, 85336)-Net in Base 7 — Upper bound on s

There is no (57, 87, 85337)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 33 385266 978516 248995 932750 893204 985284 246554 099002 663891 090707 002868 048503 > 7⁸⁷ [i]