MinT - Best Known (150−118, 150, s)-Nets in Base 9

Best Known (150−118, 150, s)-Nets in Base 9

(150−118, 150, 81)-Net over F₉ — Constructive and digital

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]

(150−118, 150, 120)-Net over F₉ — Digital

Digital (32, 150, 120)-net over F₉, using

t-expansion [i] based on digital (31, 150, 120)-net over F₉, using
- net from sequence [i] based on digital (31, 119)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
    - a curve from the manYPoints database [i]

(150−118, 150, 724)-Net in Base 9 — Upper bound on s

There is no (32, 150, 725)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 137360 281825 557591 667988 163261 317122 096887 763201 940411 472171 515767 876373 372210 268677 373012 334784 400091 626643 919265 667577 111991 464656 678098 364665 > 9¹⁵⁰ [i]