MinT - Best Known (150−78, 150, s)-Nets in Base 9

Best Known (150−78, 150, s)-Nets in Base 9

(150−78, 150, 165)-Net over F₉ — Constructive and digital

Digital (72, 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]

(150−78, 150, 234)-Net over F₉ — Digital

Digital (72, 150, 234)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−78, 150, 8981)-Net in Base 9 — Upper bound on s

There is no (72, 150, 8982)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 137214 542090 660360 449619 615176 715028 040480 666417 383765 121667 989473 033689 488041 701126 459179 858515 964547 856340 535328 808637 860001 186179 820148 066065 > 9¹⁵⁰ [i]