Best Known (36, 52, s)-Nets in Base 3
(36, 52, 114)-Net over F3 — Constructive and digital
Digital (36, 52, 114)-net over F3, using
- 31 times duplication [i] based on digital (35, 51, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 17, 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, 17, 38)-net over F27, using
(36, 52, 155)-Net over F3 — Digital
Digital (36, 52, 155)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(352, 155, F3, 16) (dual of [155, 103, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(352, 249, F3, 16) (dual of [249, 197, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(351, 243, F3, 16) (dual of [243, 192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(346, 243, F3, 14) (dual of [243, 197, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(352, 249, F3, 16) (dual of [249, 197, 17]-code), using
(36, 52, 2369)-Net in Base 3 — Upper bound on s
There is no (36, 52, 2370)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6 481404 809202 376053 247569 > 352 [i]