MinT - Best Known (150−48, 150, s)-Nets in Base 9

Best Known (150−48, 150, s)-Nets in Base 9

(150−48, 150, 740)-Net over F₉ — Constructive and digital

Digital (102, 150, 740)-net over F₉, using

t-expansion [i] based on digital (91, 150, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 75, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(150−48, 150, 2573)-Net over F₉ — Digital

Digital (102, 150, 2573)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−48, 150, 1127931)-Net in Base 9 — Upper bound on s

There is no (102, 150, 1127932)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 136891 991127 136115 361521 772040 663712 617616 166287 487634 240006 299868 070297 234287 738133 002764 950129 200391 559986 220259 807493 331278 713901 369847 315201 > 9¹⁵⁰ [i]