MinT - Best Known (122−51, 122, s)-Nets in Base 4

Best Known (122−51, 122, s)-Nets in Base 4

(122−51, 122, 130)-Net over F₄ — Constructive and digital

Digital (71, 122, 130)-net over F₄, using

8 times m-reduction [i] based on digital (71, 130, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 65, 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]

(122−51, 122, 166)-Net over F₄ — Digital

Digital (71, 122, 166)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−51, 122, 2762)-Net in Base 4 — Upper bound on s

There is no (71, 122, 2763)-net in base 4, because

1 times m-reduction [i] would yield (71, 121, 2763)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 100578 734966 730610 753047 923616 488455 817054 807116 545684 591995 801901 784344 > 4¹²¹ [i]