MinT - Best Known (101, 101+82, s)-Nets in Base 4

Best Known (101, 101+82, s)-Nets in Base 4

(101, 101+82, 130)-Net over F₄ — Constructive and digital

Digital (101, 183, 130)-net over F₄, using

7 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 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]

(101, 101+82, 188)-Net over F₄ — Digital

Digital (101, 183, 188)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+82, 2584)-Net in Base 4 — Upper bound on s

There is no (101, 183, 2585)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150 560512 877553 712918 457264 812376 301587 478921 853912 147285 838805 791207 755301 383418 831002 634955 953677 190859 888064 > 4¹⁸³ [i]