MinT - Best Known (242−141, 242, s)-Nets in Base 3

Best Known (242−141, 242, s)-Nets in Base 3

(242−141, 242, 68)-Net over F₃ — Constructive and digital

Digital (101, 242, 68)-net over F₃, using

net from sequence [i] based on digital (101, 67)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 67)-sequence over F₉, using
  - s-reduction based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(242−141, 242, 96)-Net over F₃ — Digital

Digital (101, 242, 96)-net over F₃, using

t-expansion [i] based on digital (89, 242, 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]

(242−141, 242, 524)-Net in Base 3 — Upper bound on s

There is no (101, 242, 525)-net in base 3, because

1 times m-reduction [i] would yield (101, 241, 525)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 479922 476995 977397 685177 316456 623792 070502 836129 546505 408945 972567 937407 186823 195252 500521 342136 845793 529195 248529 > 3²⁴¹ [i]