MinT - Best Known (246−67, 246, s)-Nets in Base 3

Best Known (246−67, 246, s)-Nets in Base 3

(246−67, 246, 288)-Net over F₃ — Constructive and digital

Digital (179, 246, 288)-net over F₃, using

t-expansion [i] based on digital (177, 246, 288)-net over F₃, using
- 3 times m-reduction [i] based on digital (177, 249, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 83, 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]

(246−67, 246, 734)-Net over F₃ — Digital

Digital (179, 246, 734)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−67, 246, 22907)-Net in Base 3 — Upper bound on s

There is no (179, 246, 22908)-net in base 3, because

1 times m-reduction [i] would yield (179, 245, 22908)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 785 574140 844144 095885 034112 167528 904825 584366 615392 710566 165617 780323 091530 409875 853042 777746 074458 719424 306176 759545 > 3²⁴⁵ [i]