MinT - Best Known (89, 89+62, s)-Nets in Base 4

Best Known (89, 89+62, s)-Nets in Base 4

(89, 89+62, 130)-Net over F₄ — Constructive and digital

Digital (89, 151, 130)-net over F₄, using

15 times m-reduction [i] based on digital (89, 166, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 83, 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, 89+62, 211)-Net over F₄ — Digital

Digital (89, 151, 211)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+62, 3519)-Net in Base 4 — Upper bound on s

There is no (89, 151, 3520)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 219458 469219 425884 940966 006846 344671 686824 624654 158019 663652 473451 940028 690779 115162 199237 > 4¹⁵¹ [i]