MinT - Best Known (107−82, 107, s)-Nets in Base 7

Best Known (107−82, 107, s)-Nets in Base 7

(107−82, 107, 31)-Net over F₇ — Constructive and digital

Digital (25, 107, 31)-net over F₇, using

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

(107−82, 107, 72)-Net over F₇ — Digital

Digital (25, 107, 72)-net over F₇, using

t-expansion [i] based on digital (22, 107, 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]

(107−82, 107, 405)-Net in Base 7 — Upper bound on s

There is no (25, 107, 406)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2 803180 942869 943690 426736 075088 847231 370009 500580 101859 740319 285660 685176 005196 455743 518965 > 7¹⁰⁷ [i]