MinT - Best Known (150−107, 150, s)-Nets in Base 9

Best Known (150−107, 150, s)-Nets in Base 9

(150−107, 150, 81)-Net over F₉ — Constructive and digital

Digital (43, 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]

(150−107, 150, 147)-Net over F₉ — Digital

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]

(150−107, 150, 1207)-Net in Base 9 — Upper bound on s

There is no (43, 150, 1208)-net in base 9, because

1 times m-reduction [i] would yield (43, 149, 1208)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15530 753706 130613 149781 843590 809462 392343 723234 889949 743729 193174 413078 708974 045449 452536 937857 342851 630080 705362 466472 969320 044534 218006 277825 > 9¹⁴⁹ [i]