MinT - Best Known (81−38, 81, s)-Nets in Base 7

Best Known (81−38, 81, s)-Nets in Base 7

(81−38, 81, 104)-Net over F₇ — Constructive and digital

Digital (43, 81, 104)-net over F₇, using

1 times m-reduction [i] based on digital (43, 82, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 41, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(81−38, 81, 164)-Net over F₇ — Digital

Digital (43, 81, 164)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(81−38, 81, 5282)-Net in Base 7 — Upper bound on s

There is no (43, 81, 5283)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 284 104426 206822 816227 472652 070022 329374 839760 118953 884527 032614 212815 > 7⁸¹ [i]