MinT - Best Known (164, 164+71, s)-Nets in Base 3

Best Known (164, 164+71, s)-Nets in Base 3

(164, 164+71, 246)-Net over F₃ — Constructive and digital

Digital (164, 235, 246)-net over F₃, using

3¹ times duplication [i] based on digital (163, 234, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 78, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(164, 164+71, 499)-Net over F₃ — Digital

Digital (164, 235, 499)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+71, 10733)-Net in Base 3 — Upper bound on s

There is no (164, 235, 10734)-net in base 3, because

1 times m-reduction [i] would yield (164, 234, 10734)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4437 972143 028541 490175 511798 457382 521893 902362 851058 518233 341464 579732 646628 510279 181481 594972 858408 547580 551681 > 3²³⁴ [i]