MinT - Best Known (32−26, 32, s)-Nets in Base 7

Best Known (32−26, 32, s)-Nets in Base 7

(32−26, 32, 14)-Net over F₇ — Constructive and digital

Digital (6, 32, 14)-net over F₇, using

net from sequence [i] based on digital (6, 13)-sequence over F₇, using
- Niederreiter sequence [i]

(32−26, 32, 24)-Net over F₇ — Digital

Digital (6, 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]

(32−26, 32, 105)-Net in Base 7 — Upper bound on s

There is no (6, 32, 106)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1149 048226 697462 652958 409509 > 7³² [i]
extracting embedded orthogonal array [i] would yield OA(7³², 106, S₇, 26), but
- the linear programming bound shows that MÂ â‰¥ 130789 584708 628785 701874 144733 917823 623274 123528 118400 / 114 964163 043367 900782 818009 > 7³² [i]