MinT - Best Known (80−60, 80, s)-Nets in Base 7

Best Known (80−60, 80, s)-Nets in Base 7

(80−60, 80, 28)-Net over F₇ — Constructive and digital

Digital (20, 80, 28)-net over F₇, using

net from sequence [i] based on digital (20, 27)-sequence over F₇, using
- Niederreiter sequence [i]

(80−60, 80, 54)-Net over F₇ — Digital

Digital (20, 80, 54)-net over F₇, using

t-expansion [i] based on digital (19, 80, 54)-net over F₇, using
- net from sequence [i] based on digital (19, 53)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 19 and N(F) ≥ 54, using
    - an algebraic function field by Teo [i]

(80−60, 80, 340)-Net in Base 7 — Upper bound on s

There is no (20, 80, 341)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 41 310803 728995 233241 708320 478401 571583 559333 706999 819351 467806 262905 > 7⁸⁰ [i]