Best Known (95, 95+22, s)-Nets in Base 3
(95, 95+22, 688)-Net over F3 — Constructive and digital
Digital (95, 117, 688)-net over F3, using
- 31 times duplication [i] based on digital (94, 116, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 29, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 29, 172)-net over F81, using
(95, 95+22, 3044)-Net over F3 — Digital
Digital (95, 117, 3044)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3117, 3044, F3, 2, 22) (dual of [(3044, 2), 5971, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3117, 3290, F3, 2, 22) (dual of [(3290, 2), 6463, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3117, 6580, F3, 22) (dual of [6580, 6463, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3117, 6581, F3, 22) (dual of [6581, 6464, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(3113, 6561, F3, 22) (dual of [6561, 6448, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(397, 6561, F3, 19) (dual of [6561, 6464, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(34, 20, F3, 2) (dual of [20, 16, 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
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3117, 6581, F3, 22) (dual of [6581, 6464, 23]-code), using
- OOA 2-folding [i] based on linear OA(3117, 6580, F3, 22) (dual of [6580, 6463, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(3117, 3290, F3, 2, 22) (dual of [(3290, 2), 6463, 23]-NRT-code), using
(95, 95+22, 291610)-Net in Base 3 — Upper bound on s
There is no (95, 117, 291611)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 66 556299 301714 190430 818988 564747 683474 099757 752240 729211 > 3117 [i]