MinT - Best Known (77−32, 77, s)-Nets in Base 7

Best Known (77−32, 77, s)-Nets in Base 7

(77−32, 77, 112)-Net over F₇ — Constructive and digital

Digital (45, 77, 112)-net over F₇, using

1 times m-reduction [i] based on digital (45, 78, 112)-net over F₇, using
- trace code for nets [i] based on digital (6, 39, 56)-net over F₄₉, using
  - net from sequence [i] based on digital (6, 55)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(77−32, 77, 262)-Net over F₇ — Digital

Digital (45, 77, 262)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−32, 77, 13215)-Net in Base 7 — Upper bound on s

There is no (45, 77, 13216)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 118234 146592 930850 435088 432368 492393 346232 429481 712054 584550 789121 > 7⁷⁷ [i]