Best Known (152−102, 152, s)-Nets in Base 3
(152−102, 152, 48)-Net over F3 — Constructive and digital
Digital (50, 152, 48)-net over F3, using
- t-expansion [i] based on digital (45, 152, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(152−102, 152, 64)-Net over F3 — Digital
Digital (50, 152, 64)-net over F3, using
- t-expansion [i] based on digital (49, 152, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(152−102, 152, 161)-Net over F3 — Upper bound on s (digital)
There is no digital (50, 152, 162)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(3152, 162, F3, 102) (dual of [162, 10, 103]-code), but
- residual code [i] would yield linear OA(350, 59, F3, 34) (dual of [59, 9, 35]-code), but
- 1 times truncation [i] would yield linear OA(349, 58, F3, 33) (dual of [58, 9, 34]-code), but
- residual code [i] would yield linear OA(316, 24, F3, 11) (dual of [24, 8, 12]-code), but
- 1 times truncation [i] would yield linear OA(349, 58, F3, 33) (dual of [58, 9, 34]-code), but
- residual code [i] would yield linear OA(350, 59, F3, 34) (dual of [59, 9, 35]-code), but
(152−102, 152, 215)-Net in Base 3 — Upper bound on s
There is no (50, 152, 216)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3 676357 932915 289570 322891 122749 780423 425665 373871 596161 204252 625808 198881 > 3152 [i]