MinT - Best Known (69−36, 69, s)-Nets in Base 7

Best Known (69−36, 69, s)-Nets in Base 7

(69−36, 69, 35)-Net over F₇ — Constructive and digital

Digital (33, 69, 35)-net over F₇, using

net from sequence [i] based on digital (33, 34)-sequence over F₇, using
- Niederreiter sequence [i]

(69−36, 69, 96)-Net over F₇ — Digital

Digital (33, 69, 96)-net over F₇, using

net from sequence [i] based on digital (33, 95)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 33 and N(F) ≥ 96, using
  - an algebraic function field by Teo [i]

(69−36, 69, 2173)-Net in Base 7 — Upper bound on s

There is no (33, 69, 2174)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 20522 275877 021562 139549 298820 092811 502462 842677 216318 263213 > 7⁶⁹ [i]