MinT - Best Known (101−41, 101, s)-Nets in Base 7

Best Known (101−41, 101, s)-Nets in Base 7

(101−41, 101, 118)-Net over F₇ — Constructive and digital

Digital (60, 101, 118)-net over F₇, using

1 times m-reduction [i] based on digital (60, 102, 118)-net over F₇, using
- trace code for nets [i] based on digital (9, 51, 59)-net over F₄₉, using
  - net from sequence [i] based on digital (9, 58)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(101−41, 101, 357)-Net over F₇ — Digital

Digital (60, 101, 357)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−41, 101, 23249)-Net in Base 7 — Upper bound on s

There is no (60, 101, 23250)-net in base 7, because

1 times m-reduction [i] would yield (60, 100, 23250)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 237067 198423 845481 133163 981911 506874 301741 521305 634939 177276 976114 024287 575756 434601 > 7¹⁰⁰ [i]