MinT - Best Known (70, 150, s)-Nets in Base 9

Best Known (70, 150, s)-Nets in Base 9

(70, 150, 165)-Net over F₉ — Constructive and digital

Digital (70, 150, 165)-net over F₉, using

t-expansion [i] based on digital (64, 150, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(70, 150, 211)-Net over F₉ — Digital

Digital (70, 150, 211)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 150, 7441)-Net in Base 9 — Upper bound on s

There is no (70, 150, 7442)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 136956 396385 806356 772967 221692 336572 311765 458261 745598 505709 183263 611313 251116 654457 871489 353938 123484 489617 283026 901858 439396 704275 404639 025025 > 9¹⁵⁰ [i]