MinT - Best Known (149−49, 149, s)-Nets in Base 3

Best Known (149−49, 149, s)-Nets in Base 3

(149−49, 149, 156)-Net over F₃ — Constructive and digital

Digital (100, 149, 156)-net over F₃, using

7 times m-reduction [i] based on digital (100, 156, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 78, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(149−49, 149, 259)-Net over F₃ — Digital

Digital (100, 149, 259)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−49, 149, 4267)-Net in Base 3 — Upper bound on s

There is no (100, 149, 4268)-net in base 3, because

1 times m-reduction [i] would yield (100, 148, 4268)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41162 592119 810145 661369 288368 632334 765371 848676 525992 687525 589336 484417 > 3¹⁴⁸ [i]