MinT - Best Known (230−56, 230, s)-Nets in Base 3

Best Known (230−56, 230, s)-Nets in Base 3

(230−56, 230, 400)-Net over F₃ — Constructive and digital

Digital (174, 230, 400)-net over F₃, using

3² times duplication [i] based on digital (172, 228, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 57, 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]

(230−56, 230, 1059)-Net over F₃ — Digital

Digital (174, 230, 1059)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−56, 230, 46873)-Net in Base 3 — Upper bound on s

There is no (174, 230, 46874)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 692253 683421 165618 151483 977005 692384 356576 266931 682231 923086 315597 541640 180103 622740 161644 983788 244298 449945 > 3²³⁰ [i]