MinT - Best Known (10, 10+41, s)-Nets in Base 7

Best Known (10, 10+41, s)-Nets in Base 7

(10, 10+41, 18)-Net over F₇ — Constructive and digital

Digital (10, 51, 18)-net over F₇, using

net from sequence [i] based on digital (10, 17)-sequence over F₇, using
- Niederreiter sequence [i]

(10, 10+41, 38)-Net over F₇ — Digital

Digital (10, 51, 38)-net over F₇, using

t-expansion [i] based on digital (9, 51, 38)-net over F₇, using
- net from sequence [i] based on digital (9, 37)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 9 and N(F) ≥ 38, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(10, 10+41, 153)-Net in Base 7 — Upper bound on s

There is no (10, 51, 154)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁵¹, 154, S₇, 41), but
- the linear programming bound shows that MÂ â‰¥ 3 454401 003115 769146 313735 009841 224311 056031 482306 051556 901312 391876 182833 947143 008998 992163 667478 098300 / 265812 630647 612272 142860 760043 144557 005012 196328 806175 676081 > 7⁵¹ [i]