MinT - Best Known (133−57, 133, s)-Nets in Base 4

Best Known (133−57, 133, s)-Nets in Base 4

(133−57, 133, 130)-Net over F₄ — Constructive and digital

Digital (76, 133, 130)-net over F₄, using

7 times m-reduction [i] based on digital (76, 140, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 70, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(133−57, 133, 165)-Net over F₄ — Digital

Digital (76, 133, 165)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−57, 133, 2572)-Net in Base 4 — Upper bound on s

There is no (76, 133, 2573)-net in base 4, because

1 times m-reduction [i] would yield (76, 132, 2573)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29 829395 428442 944380 123842 958984 631515 781349 411916 060268 690977 574380 559248 762400 > 4¹³² [i]