Best Known (55−16, 55, s)-Nets in Base 3
(55−16, 55, 144)-Net over F3 — Constructive and digital
Digital (39, 55, 144)-net over F3, using
- 31 times duplication [i] based on digital (38, 54, 144)-net over F3, using
- trace code for nets [i] based on digital (2, 18, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- trace code for nets [i] based on digital (2, 18, 48)-net over F27, using
(55−16, 55, 198)-Net over F3 — Digital
Digital (39, 55, 198)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(355, 198, F3, 16) (dual of [198, 143, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(355, 242, F3, 16) (dual of [242, 187, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(355, 242, F3, 16) (dual of [242, 187, 17]-code), using
(55−16, 55, 3580)-Net in Base 3 — Upper bound on s
There is no (39, 55, 3581)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 174 588920 053677 065436 217185 > 355 [i]