MinT - Best Known (32−27, 32, s)-Nets in Base 7

Best Known (32−27, 32, s)-Nets in Base 7

(32−27, 32, 13)-Net over F₇ — Constructive and digital

Digital (5, 32, 13)-net over F₇, using

net from sequence [i] based on digital (5, 12)-sequence over F₇, using
- Niederreiter sequence [i]

(32−27, 32, 24)-Net over F₇ — Digital

Digital (5, 32, 24)-net over F₇, using

t-expansion [i] based on digital (4, 32, 24)-net over F₇, using
- net from sequence [i] based on digital (4, 23)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 4 and N(F) ≥ 24, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(32−27, 32, 79)-Net in Base 7 — Upper bound on s

There is no (5, 32, 80)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7³², 80, S₇, 27), but
- the linear programming bound shows that MÂ â‰¥ 78815 867873 894723 851080 631570 918508 669971 392897 624768 196755 / 69 526651 545333 363950 584073 542909 > 7³² [i]