MinT - Best Known (232−144, 232, s)-Nets in Base 3

Best Known (232−144, 232, s)-Nets in Base 3

(232−144, 232, 63)-Net over F₃ — Constructive and digital

Digital (88, 232, 63)-net over F₃, using

net from sequence [i] based on digital (88, 62)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 62)-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]

(232−144, 232, 84)-Net over F₃ — Digital

Digital (88, 232, 84)-net over F₃, using

t-expansion [i] based on digital (71, 232, 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]

(232−144, 232, 408)-Net in Base 3 — Upper bound on s

There is no (88, 232, 409)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 499 937568 180826 443397 537014 519660 960942 253142 361221 851306 070110 127372 312664 535413 832386 535595 530151 495282 146209 > 3²³² [i]