MinT - Best Known (149, 149+48, s)-Nets in Base 3

Best Known (149, 149+48, s)-Nets in Base 3

(149, 149+48, 400)-Net over F₃ — Constructive and digital

Digital (149, 197, 400)-net over F₃, using

3¹ times duplication [i] based on digital (148, 196, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 49, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(149, 149+48, 931)-Net over F₃ — Digital

Digital (149, 197, 931)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+48, 40406)-Net in Base 3 — Upper bound on s

There is no (149, 197, 40407)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9840 823609 269191 276613 708598 398653 368503 310695 977161 974859 943550 976424 867562 986128 772691 287889 > 3¹⁹⁷ [i]