MinT - Best Known (202−59, 202, s)-Nets in Base 3

Best Known (202−59, 202, s)-Nets in Base 3

(202−59, 202, 252)-Net over F₃ — Constructive and digital

Digital (143, 202, 252)-net over F₃, using

3¹ times duplication [i] based on digital (142, 201, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 67, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(202−59, 202, 487)-Net over F₃ — Digital

Digital (143, 202, 487)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−59, 202, 11802)-Net in Base 3 — Upper bound on s

There is no (143, 202, 11803)-net in base 3, because

1 times m-reduction [i] would yield (143, 201, 11803)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 796993 875655 145933 089979 129727 208362 510472 807059 005617 593708 200965 135409 518289 077788 964558 497663 > 3²⁰¹ [i]