MinT - Best Known (62−52, 62, s)-Nets in Base 7

Best Known (62−52, 62, s)-Nets in Base 7

(62−52, 62, 18)-Net over F₇ — Constructive and digital

Digital (10, 62, 18)-net over F₇, using

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

(62−52, 62, 38)-Net over F₇ — Digital

Digital (10, 62, 38)-net over F₇, using

t-expansion [i] based on digital (9, 62, 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]

(62−52, 62, 107)-Net in Base 7 — Upper bound on s

There is no (10, 62, 108)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁶², 108, S₇, 52), but
- the linear programming bound shows that MÂ â‰¥ 34 790396 976328 978227 500974 562047 956186 076582 720255 414721 946505 827366 837190 691075 899007 102139 644287 515619 727828 514354 774645 013607 / 1374 238425 138903 634687 289595 753743 706597 084872 529962 453334 602549 762131 142447 > 7⁶² [i]