MinT - Best Known (181−49, 181, s)-Nets in Base 3

Best Known (181−49, 181, s)-Nets in Base 3

(181−49, 181, 288)-Net over F₃ — Constructive and digital

Digital (132, 181, 288)-net over F₃, using

3¹ times duplication [i] based on digital (131, 180, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 60, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(181−49, 181, 579)-Net over F₃ — Digital

Digital (132, 181, 579)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−49, 181, 18543)-Net in Base 3 — Upper bound on s

There is no (132, 181, 18544)-net in base 3, because

1 times m-reduction [i] would yield (132, 180, 18544)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 223630 487360 033093 036424 407887 271056 680242 844911 696294 726251 895497 248788 805478 448129 > 3¹⁸⁰ [i]