MinT - Best Known (182−106, 182, s)-Nets in Base 3

Best Known (182−106, 182, s)-Nets in Base 3

(182−106, 182, 51)-Net over F₃ — Constructive and digital

Digital (76, 182, 51)-net over F₃, using

net from sequence [i] based on digital (76, 50)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 50)-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]

(182−106, 182, 84)-Net over F₃ — Digital

Digital (76, 182, 84)-net over F₃, using

t-expansion [i] based on digital (71, 182, 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]

(182−106, 182, 397)-Net in Base 3 — Upper bound on s

There is no (76, 182, 398)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 701 453464 735138 212589 055794 021363 859487 091410 918493 475660 353483 484896 685242 797070 037589 > 3¹⁸² [i]