MinT - Best Known (113, 113+45, s)-Nets in Base 3

Best Known (113, 113+45, s)-Nets in Base 3

(113, 113+45, 246)-Net over F₃ — Constructive and digital

Digital (113, 158, 246)-net over F₃, using

1 times m-reduction [i] based on digital (113, 159, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 53, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(113, 113+45, 432)-Net over F₃ — Digital

Digital (113, 158, 432)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+45, 11479)-Net in Base 3 — Upper bound on s

There is no (113, 158, 11480)-net in base 3, because

1 times m-reduction [i] would yield (113, 157, 11480)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 809 986914 137832 473985 067461 868542 258844 037994 380374 860853 791924 889703 317521 > 3¹⁵⁷ [i]