MinT - Best Known (70, 166, s)-Nets in Base 3

Best Known (70, 166, s)-Nets in Base 3

(70, 166, 48)-Net over F₃ — Constructive and digital

Digital (70, 166, 48)-net over F₃, using

t-expansion [i] based on digital (45, 166, 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]

(70, 166, 82)-Net over F₃ — Digital

Digital (70, 166, 82)-net over F₃, using

t-expansion [i] based on digital (69, 166, 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]

(70, 166, 373)-Net in Base 3 — Upper bound on s

There is no (70, 166, 374)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 17 419741 833019 645125 282771 369046 706252 383080 103607 239703 255868 739427 533092 302305 > 3¹⁶⁶ [i]