Best Known (36−11, 36, s)-Nets in Base 3
(36−11, 36, 114)-Net over F3 — Constructive and digital
Digital (25, 36, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 12, 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
(36−11, 36, 142)-Net over F3 — Digital
Digital (25, 36, 142)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(336, 142, F3, 11) (dual of [142, 106, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(336, 242, F3, 11) (dual of [242, 206, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(336, 242, F3, 11) (dual of [242, 206, 12]-code), using
(36−11, 36, 2844)-Net in Base 3 — Upper bound on s
There is no (25, 36, 2845)-net in base 3, because
- 1 times m-reduction [i] would yield (25, 35, 2845)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 50096 774786 371659 > 335 [i]