MinT - Best Known (80−52, 80, s)-Nets in Base 7

Best Known (80−52, 80, s)-Nets in Base 7

(80−52, 80, 32)-Net over F₇ — Constructive and digital

Digital (28, 80, 32)-net over F₇, using

t-expansion [i] based on digital (27, 80, 32)-net over F₇, using
- net from sequence [i] based on digital (27, 31)-sequence over F₇, using
  - Niederreiter sequence [i]

(80−52, 80, 78)-Net over F₇ — Digital

Digital (28, 80, 78)-net over F₇, using

t-expansion [i] based on digital (27, 80, 78)-net over F₇, using
- net from sequence [i] based on digital (27, 77)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 27 and N(F) ≥ 78, using
    - an algebraic function field by Teo [i]

(80−52, 80, 683)-Net in Base 7 — Upper bound on s

There is no (28, 80, 684)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 40 758545 661596 788511 024984 116380 559150 468728 234089 580088 048656 627145 > 7⁸⁰ [i]