Best Known (121, 155, s)-Nets in Base 3
(121, 155, 600)-Net over F3 — Constructive and digital
Digital (121, 155, 600)-net over F3, using
- 1 times m-reduction [i] based on digital (121, 156, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 39, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 39, 150)-net over F81, using
(121, 155, 1236)-Net over F3 — Digital
Digital (121, 155, 1236)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3155, 1236, F3, 34) (dual of [1236, 1081, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using
(121, 155, 80361)-Net in Base 3 — Upper bound on s
There is no (121, 155, 80362)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 89 912388 390090 488599 537888 890468 759021 041917 213196 213170 808766 352156 108341 > 3155 [i]