Best Known (63, 85, s)-Nets in Base 3
(63, 85, 228)-Net over F3 — Constructive and digital
Digital (63, 85, 228)-net over F3, using
- 31 times duplication [i] based on digital (62, 84, 228)-net over F3, using
- trace code for nets [i] based on digital (6, 28, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- trace code for nets [i] based on digital (6, 28, 76)-net over F27, using
(63, 85, 402)-Net over F3 — Digital
Digital (63, 85, 402)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(385, 402, F3, 22) (dual of [402, 317, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(385, 728, F3, 22) (dual of [728, 643, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 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(385, 728, F3, 22) (dual of [728, 643, 23]-code), using
(63, 85, 11924)-Net in Base 3 — Upper bound on s
There is no (63, 85, 11925)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 35926 877425 589402 443195 959463 696500 408011 > 385 [i]