MinT - Best Known (115, 188, s)-Nets in Base 3

Best Known (115, 188, s)-Nets in Base 3

(115, 188, 148)-Net over F₃ — Constructive and digital

Digital (115, 188, 148)-net over F₃, using

8 times m-reduction [i] based on digital (115, 196, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 98, 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]

(115, 188, 193)-Net over F₃ — Digital

Digital (115, 188, 193)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 188, 2113)-Net in Base 3 — Upper bound on s

There is no (115, 188, 2114)-net in base 3, because

1 times m-reduction [i] would yield (115, 187, 2114)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 169405 579858 592124 432471 965200 333044 663942 163585 054882 759857 681151 549358 372238 730320 327273 > 3¹⁸⁷ [i]