MinT - Best Known (76−51, 76, s)-Nets in Base 7

Best Known (76−51, 76, s)-Nets in Base 7

(76−51, 76, 31)-Net over F₇ — Constructive and digital

Digital (25, 76, 31)-net over F₇, using

net from sequence [i] based on digital (25, 30)-sequence over F₇, using
- Niederreiter sequence [i]

(76−51, 76, 72)-Net over F₇ — Digital

Digital (25, 76, 72)-net over F₇, using

t-expansion [i] based on digital (22, 76, 72)-net over F₇, using
- net from sequence [i] based on digital (22, 71)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 22 and N(F) ≥ 72, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(76−51, 76, 565)-Net in Base 7 — Upper bound on s

There is no (25, 76, 566)-net in base 7, because

1 times m-reduction [i] would yield (25, 75, 566)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2435 837813 918431 489229 392686 161729 196305 525967 575066 349349 953109 > 7⁷⁵ [i]