MinT - Best Known (63−54, 63, s)-Nets in Base 7

Best Known (63−54, 63, s)-Nets in Base 7

(63−54, 63, 17)-Net over F₇ — Constructive and digital

Digital (9, 63, 17)-net over F₇, using

net from sequence [i] based on digital (9, 16)-sequence over F₇, using
- Niederreiter sequence [i]

(63−54, 63, 38)-Net over F₇ — Digital

Digital (9, 63, 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]

(63−54, 63, 74)-Net in Base 7 — Upper bound on s

There is no (9, 63, 75)-net in base 7, because

1 times m-reduction [i] would yield (9, 62, 75)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7⁶², 75, S₇, 53), but
  - the linear programming bound shows that MÂ â‰¥ 1973 331294 291885 342482 074010 387060 867505 270283 381542 221967 639077 / 65958 050304 > 7⁶² [i]