MinT - Best Known (77−31, 77, s)-Nets in Base 7

Best Known (77−31, 77, s)-Nets in Base 7

(77−31, 77, 114)-Net over F₇ — Constructive and digital

Digital (46, 77, 114)-net over F₇, using

1 times m-reduction [i] based on digital (46, 78, 114)-net over F₇, using
- trace code for nets [i] based on digital (7, 39, 57)-net over F₄₉, using
  - net from sequence [i] based on digital (7, 56)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(77−31, 77, 304)-Net over F₇ — Digital

Digital (46, 77, 304)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−31, 77, 20475)-Net in Base 7 — Upper bound on s

There is no (46, 77, 20476)-net in base 7, because

1 times m-reduction [i] would yield (46, 76, 20476)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 16883 683793 796474 537047 756314 353241 669925 928394 767376 199482 463713 > 7⁷⁶ [i]