MinT - Best Known (158, 158+71, s)-Nets in Base 3

Best Known (158, 158+71, s)-Nets in Base 3

(158, 158+71, 204)-Net over F₃ — Constructive and digital

Digital (158, 229, 204)-net over F₃, using

3¹ times duplication [i] based on digital (157, 228, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 76, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(158, 158+71, 450)-Net over F₃ — Digital

Digital (158, 229, 450)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+71, 8885)-Net in Base 3 — Upper bound on s

There is no (158, 229, 8886)-net in base 3, because

1 times m-reduction [i] would yield (158, 228, 8886)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 100203 726350 263917 678540 971447 637239 943165 618180 985933 652718 398826 073224 041642 950079 518693 897426 318858 143201 > 3²²⁸ [i]