MinT - Best Known (48−39, 48, s)-Nets in Base 7

Best Known (48−39, 48, s)-Nets in Base 7

(48−39, 48, 17)-Net over F₇ — Constructive and digital

Digital (9, 48, 17)-net over F₇, using

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

(48−39, 48, 38)-Net over F₇ — Digital

Digital (9, 48, 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]

(48−39, 48, 136)-Net in Base 7 — Upper bound on s

There is no (9, 48, 137)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁴⁸, 137, S₇, 39), but
- the linear programming bound shows that MÂ â‰¥ 3634 622082 341968 144354 451302 618954 379598 431252 689595 662542 322982 590659 679383 326226 735462 000000 / 96171 216555 119780 182912 851149 442416 995574 869805 886037 > 7⁴⁸ [i]