Best Known (8, 24, s)-Nets in Base 3
(8, 24, 16)-Net over F3 — Constructive and digital
Digital (8, 24, 16)-net over F3, using
- t-expansion [i] based on digital (7, 24, 16)-net over F3, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 7 and N(F) ≥ 16, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
(8, 24, 17)-Net over F3 — Digital
Digital (8, 24, 17)-net over F3, using
- net from sequence [i] based on digital (8, 16)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 8 and N(F) ≥ 17, using
(8, 24, 36)-Net over F3 — Upper bound on s (digital)
There is no digital (8, 24, 37)-net over F3, because
- 1 times m-reduction [i] would yield digital (8, 23, 37)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(323, 37, F3, 15) (dual of [37, 14, 16]-code), but
- construction Y1 [i] would yield
- linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- “HHM†bound on codes from Brouwer’s database [i]
- linear OA(314, 37, F3, 9) (dual of [37, 23, 10]-code), but
- discarding factors / shortening the dual code would yield linear OA(314, 31, F3, 9) (dual of [31, 17, 10]-code), but
- linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- construction Y1 [i] would yield
- extracting embedded orthogonal array [i] would yield linear OA(323, 37, F3, 15) (dual of [37, 14, 16]-code), but
(8, 24, 43)-Net in Base 3 — Upper bound on s
There is no (8, 24, 44)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 293627 094465 > 324 [i]