MinT - Best Known (113, 113+39, s)-Nets in Base 3

Best Known (113, 113+39, s)-Nets in Base 3

(113, 113+39, 288)-Net over F₃ — Constructive and digital

Digital (113, 152, 288)-net over F₃, using

1 times m-reduction [i] based on digital (113, 153, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 51, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(113, 113+39, 617)-Net over F₃ — Digital

Digital (113, 152, 617)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+39, 24531)-Net in Base 3 — Upper bound on s

There is no (113, 152, 24532)-net in base 3, because

1 times m-reduction [i] would yield (113, 151, 24532)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 110758 956945 253427 762812 052340 607460 298636 923109 987642 249867 013052 390897 > 3¹⁵¹ [i]