MinT - Best Known (148−98, 148, s)-Nets in Base 9

Best Known (148−98, 148, s)-Nets in Base 9

(148−98, 148, 81)-Net over F₉ — Constructive and digital

Digital (50, 148, 81)-net over F₉, using

t-expansion [i] based on digital (32, 148, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(148−98, 148, 182)-Net over F₉ — Digital

Digital (50, 148, 182)-net over F₉, using

net from sequence [i] based on digital (50, 181)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
  - a curve from the manYPoints database [i]

(148−98, 148, 1791)-Net in Base 9 — Upper bound on s

There is no (50, 148, 1792)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1713 739366 515477 744976 093882 437103 609972 618315 322426 601217 224443 559586 555201 739627 902186 786356 297464 020531 626793 677169 547733 530458 895965 730817 > 9¹⁴⁸ [i]