MinT - Best Known (202−115, 202, s)-Nets in Base 3

Best Known (202−115, 202, s)-Nets in Base 3

(202−115, 202, 62)-Net over F₃ — Constructive and digital

Digital (87, 202, 62)-net over F₃, using

net from sequence [i] based on digital (87, 61)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 61)-sequence over F₉, using
  - s-reduction 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]

(202−115, 202, 84)-Net over F₃ — Digital

Digital (87, 202, 84)-net over F₃, using

t-expansion [i] based on digital (71, 202, 84)-net over F₃, using
- net from sequence [i] based on digital (71, 83)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(202−115, 202, 477)-Net in Base 3 — Upper bound on s

There is no (87, 202, 478)-net in base 3, because

1 times m-reduction [i] would yield (87, 201, 478)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 859582 691987 623802 907502 337214 157848 394693 862130 463731 840230 361052 144429 103791 855204 829423 496141 > 3²⁰¹ [i]