MinT - Best Known (61, 61+40, s)-Nets in Base 7

Best Known (61, 61+40, s)-Nets in Base 7

(61, 61+40, 120)-Net over F₇ — Constructive and digital

Digital (61, 101, 120)-net over F₇, using

1 times m-reduction [i] based on digital (61, 102, 120)-net over F₇, using
- trace code for nets [i] based on digital (10, 51, 60)-net over F₄₉, using
  - net from sequence [i] based on digital (10, 59)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(61, 61+40, 399)-Net over F₇ — Digital

Digital (61, 101, 399)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+40, 25626)-Net in Base 7 — Upper bound on s

There is no (61, 101, 25627)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 22 657064 414806 277757 357143 269765 619358 418398 821096 177125 875052 945258 203575 256437 093161 > 7¹⁰¹ [i]