MinT - Best Known (242−100, 242, s)-Nets in Base 3

Best Known (242−100, 242, s)-Nets in Base 3

(242−100, 242, 148)-Net over F₃ — Constructive and digital

Digital (142, 242, 148)-net over F₃, using

8 times m-reduction [i] based on digital (142, 250, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 125, 74)-net over F₉, using
  - net from sequence [i] 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]

(242−100, 242, 202)-Net over F₃ — Digital

Digital (142, 242, 202)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−100, 242, 1936)-Net in Base 3 — Upper bound on s

There is no (142, 242, 1937)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 329331 080122 439937 134148 894429 556261 267913 340906 008654 729133 418318 482631 187899 140252 346457 608298 670683 140749 498217 > 3²⁴² [i]