MinT - Best Known (37, 37+34, s)-Nets in Base 7

Best Known (37, 37+34, s)-Nets in Base 7

(37, 37+34, 102)-Net over F₇ — Constructive and digital

Digital (37, 71, 102)-net over F₇, using

1 times m-reduction [i] based on digital (37, 72, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 36, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(37, 37+34, 137)-Net over F₇ — Digital

Digital (37, 71, 137)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(37, 37+34, 4037)-Net in Base 7 — Upper bound on s

There is no (37, 71, 4038)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1 004832 660875 206724 752774 858788 942029 987059 543089 118863 574789 > 7⁷¹ [i]