MinT - Best Known (61, 61+41, s)-Nets in Base 4

Best Known (61, 61+41, s)-Nets in Base 4

(61, 61+41, 130)-Net over F₄ — Constructive and digital

Digital (61, 102, 130)-net over F₄, using

8 times m-reduction [i] based on digital (61, 110, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 55, 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]

(61, 61+41, 165)-Net over F₄ — Digital

Digital (61, 102, 165)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+41, 3021)-Net in Base 4 — Upper bound on s

There is no (61, 102, 3022)-net in base 4, because

1 times m-reduction [i] would yield (61, 101, 3022)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 433355 054714 690604 059942 081306 326234 983956 102300 601307 992916 > 4¹⁰¹ [i]