Best Known (82−22, 82, s)-Nets in Base 3
(82−22, 82, 204)-Net over F3 — Constructive and digital
Digital (60, 82, 204)-net over F3, using
- 31 times duplication [i] based on digital (59, 81, 204)-net over F3, using
- trace code for nets [i] based on digital (5, 27, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- trace code for nets [i] based on digital (5, 27, 68)-net over F27, using
(82−22, 82, 339)-Net over F3 — Digital
Digital (60, 82, 339)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(382, 339, F3, 22) (dual of [339, 257, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(382, 364, F3, 22) (dual of [364, 282, 23]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 364 | 36−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(382, 364, F3, 22) (dual of [364, 282, 23]-code), using
(82−22, 82, 8834)-Net in Base 3 — Upper bound on s
There is no (60, 82, 8835)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1330 814938 693089 977730 338807 230932 893211 > 382 [i]