Best Known (119, 119+28, s)-Nets in Base 3
(119, 119+28, 688)-Net over F3 — Constructive and digital
Digital (119, 147, 688)-net over F3, using
- t-expansion [i] based on digital (118, 147, 688)-net over F3, using
- 1 times m-reduction [i] based on digital (118, 148, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 37, 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, 37, 172)-net over F81, using
- 1 times m-reduction [i] based on digital (118, 148, 688)-net over F3, using
(119, 119+28, 2954)-Net over F3 — Digital
Digital (119, 147, 2954)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3147, 2954, F3, 2, 28) (dual of [(2954, 2), 5761, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3147, 3286, F3, 2, 28) (dual of [(3286, 2), 6425, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3147, 6572, F3, 28) (dual of [6572, 6425, 29]-code), using
- construction XX applied to Ce(27) ⊂ Ce(25) ⊂ Ce(24) [i] based on
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3137, 6561, F3, 26) (dual of [6561, 6424, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3129, 6561, F3, 25) (dual of [6561, 6432, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(27) ⊂ Ce(25) ⊂ Ce(24) [i] based on
- OOA 2-folding [i] based on linear OA(3147, 6572, F3, 28) (dual of [6572, 6425, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(3147, 3286, F3, 2, 28) (dual of [(3286, 2), 6425, 29]-NRT-code), using
(119, 119+28, 309159)-Net in Base 3 — Upper bound on s
There is no (119, 147, 309160)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 13703 870826 501736 269491 684012 183277 504603 819542 419635 292442 690441 172081 > 3147 [i]