Best Known (122, 122+28, s)-Nets in Base 3
(122, 122+28, 688)-Net over F3 — Constructive and digital
Digital (122, 150, 688)-net over F3, using
- t-expansion [i] based on digital (121, 150, 688)-net over F3, using
- 2 times m-reduction [i] based on digital (121, 152, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 38, 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, 38, 172)-net over F81, using
- 2 times m-reduction [i] based on digital (121, 152, 688)-net over F3, using
(122, 122+28, 3291)-Net over F3 — Digital
Digital (122, 150, 3291)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3150, 3291, F3, 2, 28) (dual of [(3291, 2), 6432, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3150, 6582, F3, 28) (dual of [6582, 6432, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3149, 6581, F3, 28) (dual of [6581, 6432, 29]-code), using
- construction X applied to Ce(27) ⊂ 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(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(34, 20, F3, 2) (dual of [20, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3149, 6581, F3, 28) (dual of [6581, 6432, 29]-code), using
- OOA 2-folding [i] based on linear OA(3150, 6582, F3, 28) (dual of [6582, 6432, 29]-code), using
(122, 122+28, 391224)-Net in Base 3 — Upper bound on s
There is no (122, 150, 391225)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 369993 229044 783340 710440 642604 875321 748665 161279 187331 610145 099894 030121 > 3150 [i]