MinT - Best Known (160−66, 160, s)-Nets in Base 4

Best Known (160−66, 160, s)-Nets in Base 4

(160−66, 160, 130)-Net over F₄ — Constructive and digital

Digital (94, 160, 130)-net over F₄, using

16 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 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]

(160−66, 160, 218)-Net over F₄ — Digital

Digital (94, 160, 218)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−66, 160, 3614)-Net in Base 4 — Upper bound on s

There is no (94, 160, 3615)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 139106 624106 864037 240165 668745 322237 698061 493373 222947 725360 970814 701928 554803 026184 845655 916320 > 4¹⁶⁰ [i]