Best Known (115, 141, s)-Nets in Base 3
(115, 141, 688)-Net over F3 — Constructive and digital
Digital (115, 141, 688)-net over F3, using
- 3 times m-reduction [i] based on digital (115, 144, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 36, 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, 36, 172)-net over F81, using
(115, 141, 3290)-Net over F3 — Digital
Digital (115, 141, 3290)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3141, 3290, F3, 2, 26) (dual of [(3290, 2), 6439, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3141, 6580, F3, 26) (dual of [6580, 6439, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3141, 6581, F3, 26) (dual of [6581, 6440, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3137, 6561, F3, 26) (dual of [6561, 6424, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3121, 6561, F3, 23) (dual of [6561, 6440, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3141, 6581, F3, 26) (dual of [6581, 6440, 27]-code), using
- OOA 2-folding [i] based on linear OA(3141, 6580, F3, 26) (dual of [6580, 6439, 27]-code), using
(115, 141, 423929)-Net in Base 3 — Upper bound on s
There is no (115, 141, 423930)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 18 797498 553989 808866 095739 137001 705704 180200 952639 418337 113801 102589 > 3141 [i]