Best Known (247−46, 247, s)-Nets in Base 3
(247−46, 247, 896)-Net over F3 — Constructive and digital
Digital (201, 247, 896)-net over F3, using
- t-expansion [i] based on digital (199, 247, 896)-net over F3, using
- 1 times m-reduction [i] based on digital (199, 248, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 62, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 62, 224)-net over F81, using
- 1 times m-reduction [i] based on digital (199, 248, 896)-net over F3, using
(247−46, 247, 3971)-Net over F3 — Digital
Digital (201, 247, 3971)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3247, 3971, F3, 46) (dual of [3971, 3724, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(3247, 6584, F3, 46) (dual of [6584, 6337, 47]-code), using
- construction XX applied to Ce(45) ⊂ Ce(42) ⊂ Ce(40) [i] based on
- linear OA(3241, 6561, F3, 46) (dual of [6561, 6320, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3225, 6561, F3, 43) (dual of [6561, 6336, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(34, 21, F3, 2) (dual of [21, 17, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(45) ⊂ Ce(42) ⊂ Ce(40) [i] based on
- discarding factors / shortening the dual code based on linear OA(3247, 6584, F3, 46) (dual of [6584, 6337, 47]-code), using
(247−46, 247, 627015)-Net in Base 3 — Upper bound on s
There is no (201, 247, 627016)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 7062 561334 139139 290855 004681 081006 662503 257052 882185 131315 747051 906163 014303 087583 687393 484589 388868 283152 524695 873121 > 3247 [i]