MinT - Best Known (146−82, 146, s)-Nets in Base 3

Best Known (146−82, 146, s)-Nets in Base 3

(146−82, 146, 48)-Net over F₃ — Constructive and digital

Digital (64, 146, 48)-net over F₃, using

t-expansion [i] based on digital (45, 146, 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]

(146−82, 146, 64)-Net over F₃ — Digital

Digital (64, 146, 64)-net over F₃, using

t-expansion [i] based on digital (49, 146, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(146−82, 146, 364)-Net in Base 3 — Upper bound on s

There is no (64, 146, 365)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4728 638286 796111 684842 925214 709709 219775 852146 020321 250739 392531 182651 > 3¹⁴⁶ [i]