MinT - Best Known (97−36, 97, s)-Nets in Base 7

Best Known (97−36, 97, s)-Nets in Base 7

(97−36, 97, 124)-Net over F₇ — Constructive and digital

Digital (61, 97, 124)-net over F₇, using

1 times m-reduction [i] based on digital (61, 98, 124)-net over F₇, using
- trace code for nets [i] based on digital (12, 49, 62)-net over F₄₉, using
  - net from sequence [i] based on digital (12, 61)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(97−36, 97, 527)-Net over F₇ — Digital

Digital (61, 97, 527)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−36, 97, 45082)-Net in Base 7 — Upper bound on s

There is no (61, 97, 45083)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 9432 041151 127576 304995 072791 225645 595554 304463 700424 031965 610196 195805 944423 461005 > 7⁹⁷ [i]