MinT - Best Known (113, 113+89, s)-Nets in Base 3

Best Known (113, 113+89, s)-Nets in Base 3

(113, 113+89, 80)-Net over F₃ — Constructive and digital

Digital (113, 202, 80)-net over F₃, using

8 times m-reduction [i] based on digital (113, 210, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 105, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(113, 113+89, 144)-Net over F₃ — Digital

Digital (113, 202, 144)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+89, 1261)-Net in Base 3 — Upper bound on s

There is no (113, 202, 1262)-net in base 3, because

1 times m-reduction [i] would yield (113, 201, 1262)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 805755 840736 209693 477892 383727 122165 729991 493322 920092 687037 293313 338974 068646 298435 290411 408921 > 3²⁰¹ [i]