MinT - Best Known (157−57, 157, s)-Nets in Base 3

Best Known (157−57, 157, s)-Nets in Base 3

(157−57, 157, 148)-Net over F₃ — Constructive and digital

Digital (100, 157, 148)-net over F₃, using

9 times m-reduction [i] based on digital (100, 166, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 83, 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]

(157−57, 157, 200)-Net over F₃ — Digital

Digital (100, 157, 200)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−57, 157, 2544)-Net in Base 3 — Upper bound on s

There is no (100, 157, 2545)-net in base 3, because

1 times m-reduction [i] would yield (100, 156, 2545)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 271 689178 346406 712572 333389 372511 843294 389926 456374 370950 309172 197950 197425 > 3¹⁵⁶ [i]