MinT - Best Known (101, 101+64, s)-Nets in Base 4

Best Known (101, 101+64, s)-Nets in Base 4

(101, 101+64, 130)-Net over F₄ — Constructive and digital

Digital (101, 165, 130)-net over F₄, using

25 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+64, 275)-Net over F₄ — Digital

Digital (101, 165, 275)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+64, 5395)-Net in Base 4 — Upper bound on s

There is no (101, 165, 5396)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2193 390595 522088 899723 133586 858097 768732 410292 688988 596233 069257 818517 018528 076014 537255 997249 704904 > 4¹⁶⁵ [i]