Best Known (32, 32+14, s)-Nets in Base 3
(32, 32+14, 114)-Net over F3 — Constructive and digital
Digital (32, 46, 114)-net over F3, using
- 31 times duplication [i] based on digital (31, 45, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 15, 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
- trace code for nets [i] based on digital (1, 15, 38)-net over F27, using
(32, 32+14, 153)-Net over F3 — Digital
Digital (32, 46, 153)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(346, 153, F3, 14) (dual of [153, 107, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(346, 242, F3, 14) (dual of [242, 196, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(346, 242, F3, 14) (dual of [242, 196, 15]-code), using
(32, 32+14, 2301)-Net in Base 3 — Upper bound on s
There is no (32, 46, 2302)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 8873 163268 115993 312313 > 346 [i]