MinT - Best Known (150−105, 150, s)-Nets in Base 9

Best Known (150−105, 150, s)-Nets in Base 9

(150−105, 150, 81)-Net over F₉ — Constructive and digital

Digital (45, 150, 81)-net over F₉, using

t-expansion [i] based on digital (32, 150, 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]

(150−105, 150, 147)-Net over F₉ — Digital

Digital (45, 150, 147)-net over F₉, using

t-expansion [i] based on digital (43, 150, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(150−105, 150, 1339)-Net in Base 9 — Upper bound on s

There is no (45, 150, 1340)-net in base 9, because

1 times m-reduction [i] would yield (45, 149, 1340)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15591 535317 699328 233874 486437 336573 048243 757538 379400 700641 958945 752540 705008 195738 906685 943660 921179 054551 122773 323908 971219 099606 322644 625025 > 9¹⁴⁹ [i]