MinT - Best Known (200−66, 200, s)-Nets in Base 3

Best Known (200−66, 200, s)-Nets in Base 3

(200−66, 200, 162)-Net over F₃ — Constructive and digital

Digital (134, 200, 162)-net over F₃, using

4 times m-reduction [i] based on digital (134, 204, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 102, 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]

(200−66, 200, 329)-Net over F₃ — Digital

Digital (134, 200, 329)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−66, 200, 5095)-Net in Base 3 — Upper bound on s

There is no (134, 200, 5096)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 265917 194594 219863 931431 467838 608357 048653 479552 173567 224554 754303 303932 073701 637317 131559 508433 > 3²⁰⁰ [i]