MinT - Best Known (69−51, 69, s)-Nets in Base 7

Best Known (69−51, 69, s)-Nets in Base 7

(69−51, 69, 26)-Net over F₇ — Constructive and digital

Digital (18, 69, 26)-net over F₇, using

net from sequence [i] based on digital (18, 25)-sequence over F₇, using
- Niederreiter sequence [i]

(69−51, 69, 51)-Net over F₇ — Digital

Digital (18, 69, 51)-net over F₇, using

net from sequence [i] based on digital (18, 50)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 18 and N(F) ≥ 51, using
  - an algebraic function field by Teo [i]

(69−51, 69, 321)-Net in Base 7 — Upper bound on s

There is no (18, 69, 322)-net in base 7, because

1 times m-reduction [i] would yield (18, 68, 322)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3044 744966 916790 624627 717483 320227 127689 045040 860210 864989 > 7⁶⁸ [i]