MinT - Best Known (193−104, 193, s)-Nets in Base 3

Best Known (193−104, 193, s)-Nets in Base 3

(193−104, 193, 64)-Net over F₃ — Constructive and digital

Digital (89, 193, 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]

(193−104, 193, 96)-Net over F₃ — Digital

Digital (89, 193, 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]

(193−104, 193, 546)-Net in Base 3 — Upper bound on s

There is no (89, 193, 547)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 122 287054 491139 811115 988248 419243 860825 073952 836359 645948 313126 776891 861534 019107 793219 049081 > 3¹⁹³ [i]