MinT - Best Known (181−42, 181, s)-Nets in Base 3

Best Known (181−42, 181, s)-Nets in Base 3

(181−42, 181, 464)-Net over F₃ — Constructive and digital

Digital (139, 181, 464)-net over F₃, using

3¹ times duplication [i] based on digital (138, 180, 464)-net over F₃, using
- t-expansion [i] based on digital (137, 180, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 45, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]

(181−42, 181, 1051)-Net over F₃ — Digital

Digital (139, 181, 1051)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−42, 181, 56186)-Net in Base 3 — Upper bound on s

There is no (139, 181, 56187)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 541536 059014 494005 574568 369626 176385 158210 930547 948650 208003 066205 630975 797039 669775 > 3¹⁸¹ [i]