MinT - Best Known (246−153, 246, s)-Nets in Base 3

Best Known (246−153, 246, s)-Nets in Base 3

(246−153, 246, 64)-Net over F₃ — Constructive and digital

Digital (93, 246, 64)-net over F₃, using

t-expansion [i] based on digital (89, 246, 64)-net over F₃, using
- net from sequence [i] based on digital (89, 63)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(246−153, 246, 96)-Net over F₃ — Digital

Digital (93, 246, 96)-net over F₃, using

t-expansion [i] based on digital (89, 246, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(246−153, 246, 431)-Net in Base 3 — Upper bound on s

There is no (93, 246, 432)-net in base 3, because

1 times m-reduction [i] would yield (93, 245, 432)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 853 074914 415065 110039 390478 744400 589175 571282 400118 041007 705723 807535 867962 908049 982260 859877 429617 742891 386519 400065 > 3²⁴⁵ [i]