MinT - Best Known (89−32, 89, s)-Nets in Base 4

Best Known (89−32, 89, s)-Nets in Base 4

(89−32, 89, 130)-Net over F₄ — Constructive and digital

Digital (57, 89, 130)-net over F₄, using

13 times m-reduction [i] based on digital (57, 102, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 51, 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]

(89−32, 89, 216)-Net over F₄ — Digital

Digital (57, 89, 216)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−32, 89, 5049)-Net in Base 4 — Upper bound on s

There is no (57, 89, 5050)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 383355 111266 690616 577783 179022 284022 131429 454267 217041 > 4⁸⁹ [i]