MinT - Best Known (164−94, 164, s)-Nets in Base 3

Best Known (164−94, 164, s)-Nets in Base 3

(164−94, 164, 48)-Net over F₃ — Constructive and digital

Digital (70, 164, 48)-net over F₃, using

t-expansion [i] based on digital (45, 164, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(164−94, 164, 82)-Net over F₃ — Digital

Digital (70, 164, 82)-net over F₃, using

t-expansion [i] based on digital (69, 164, 82)-net over F₃, using
- net from sequence [i] based on digital (69, 81)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 69 and N(F) ≥ 82, using
    - Drinfeld modules of rank 1 [i]

(164−94, 164, 380)-Net in Base 3 — Upper bound on s

There is no (70, 164, 381)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 967947 170992 109627 711058 382335 491580 565914 741080 703142 055581 157518 132764 400859 > 3¹⁶⁴ [i]