Best Known (134, 134+28, s)-Nets in Base 3
(134, 134+28, 704)-Net over F3 — Constructive and digital
Digital (134, 162, 704)-net over F3, using
- 31 times duplication [i] based on digital (133, 161, 704)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (7, 21, 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
- digital (112, 140, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 35, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 35, 172)-net over F81, using
- digital (7, 21, 16)-net over F3, using
- (u, u+v)-construction [i] based on
(134, 134+28, 4920)-Net over F3 — Digital
Digital (134, 162, 4920)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3162, 4920, F3, 2, 28) (dual of [(4920, 2), 9678, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3162, 9840, F3, 28) (dual of [9840, 9678, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3162, 9841, F3, 28) (dual of [9841, 9679, 29]-code), using
- OOA 2-folding [i] based on linear OA(3162, 9840, F3, 28) (dual of [9840, 9678, 29]-code), using
(134, 134+28, 1003220)-Net in Base 3 — Upper bound on s
There is no (134, 162, 1003221)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 196628 292161 046667 783180 127158 049477 494513 479216 247849 931991 849721 845343 852161 > 3162 [i]