MinT - Best Known (149−103, 149, s)-Nets in Base 9

Best Known (149−103, 149, s)-Nets in Base 9

(149−103, 149, 81)-Net over F₉ — Constructive and digital

Digital (46, 149, 81)-net over F₉, using

t-expansion [i] based on digital (32, 149, 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]

(149−103, 149, 162)-Net over F₉ — Digital

Digital (46, 149, 162)-net over F₉, using

net from sequence [i] based on digital (46, 161)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(149−103, 149, 1427)-Net in Base 9 — Upper bound on s

There is no (46, 149, 1428)-net in base 9, because

1 times m-reduction [i] would yield (46, 148, 1428)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1723 812555 206111 589130 734395 003475 791855 514254 836591 652863 344564 352981 705901 778728 370943 459967 947688 579399 631890 169447 731067 625643 439418 013025 > 9¹⁴⁸ [i]