Best Known (158, 191, s)-Nets in Base 3
(158, 191, 896)-Net over F3 — Constructive and digital
Digital (158, 191, 896)-net over F3, using
- t-expansion [i] based on digital (157, 191, 896)-net over F3, using
- 1 times m-reduction [i] based on digital (157, 192, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 48, 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, 48, 224)-net over F81, using
- 1 times m-reduction [i] based on digital (157, 192, 896)-net over F3, using
(158, 191, 5186)-Net over F3 — Digital
Digital (158, 191, 5186)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3191, 5186, F3, 33) (dual of [5186, 4995, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3191, 6614, F3, 33) (dual of [6614, 6423, 34]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- 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(314, 53, F3, 6) (dual of [53, 39, 7]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3191, 6614, F3, 33) (dual of [6614, 6423, 34]-code), using
(158, 191, 1575140)-Net in Base 3 — Upper bound on s
There is no (158, 191, 1575141)-net in base 3, because
- 1 times m-reduction [i] would yield (158, 190, 1575141)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 4 498209 635911 128214 196074 167928 225225 236431 781597 352367 108932 311433 029027 226213 492351 477185 > 3190 [i]