MinT - Best Known (73−29, 73, s)-Nets in Base 7

Best Known (73−29, 73, s)-Nets in Base 7

(73−29, 73, 114)-Net over F₇ — Constructive and digital

Digital (44, 73, 114)-net over F₇, using

1 times m-reduction [i] based on digital (44, 74, 114)-net over F₇, using
- trace code for nets [i] based on digital (7, 37, 57)-net over F₄₉, using
  - net from sequence [i] based on digital (7, 56)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(73−29, 73, 312)-Net over F₇ — Digital

Digital (44, 73, 312)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−29, 73, 22353)-Net in Base 7 — Upper bound on s

There is no (44, 73, 22354)-net in base 7, because

1 times m-reduction [i] would yield (44, 72, 22354)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7 032089 970192 836023 865376 267862 695164 253935 633484 118752 121213 > 7⁷² [i]