MinT - Best Known (41, 41+30, s)-Nets in Base 7

Best Known (41, 41+30, s)-Nets in Base 7

(41, 41+30, 110)-Net over F₇ — Constructive and digital

Digital (41, 71, 110)-net over F₇, using

1 times m-reduction [i] based on digital (41, 72, 110)-net over F₇, using
- trace code for nets [i] based on digital (5, 36, 55)-net over F₄₉, using
  - net from sequence [i] based on digital (5, 54)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(41, 41+30, 230)-Net over F₇ — Digital

Digital (41, 71, 230)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(41, 41+30, 10699)-Net in Base 7 — Upper bound on s

There is no (41, 71, 10700)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1 005322 454938 730531 814417 690406 744607 272015 893205 114511 460961 > 7⁷¹ [i]