Best Known (30−9, 30, s)-Nets in Base 3
(30−9, 30, 114)-Net over F3 — Constructive and digital
Digital (21, 30, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 10, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
(30−9, 30, 155)-Net over F3 — Digital
Digital (21, 30, 155)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(330, 155, F3, 9) (dual of [155, 125, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(330, 242, F3, 9) (dual of [242, 212, 10]-code), using
- the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(330, 242, F3, 9) (dual of [242, 212, 10]-code), using
(30−9, 30, 3181)-Net in Base 3 — Upper bound on s
There is no (21, 30, 3182)-net in base 3, because
- 1 times m-reduction [i] would yield (21, 29, 3182)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 68 646484 557577 > 329 [i]