Best Known (168, 200, s)-Nets in Base 3
(168, 200, 1480)-Net over F3 — Constructive and digital
Digital (168, 200, 1480)-net over F3, using
- t-expansion [i] based on digital (166, 200, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 50, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 50, 370)-net over F81, using
(168, 200, 9861)-Net over F3 — Digital
Digital (168, 200, 9861)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3200, 9861, F3, 2, 32) (dual of [(9861, 2), 19522, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3200, 19722, F3, 32) (dual of [19722, 19522, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(25) [i] based on
- linear OA(3190, 19683, F3, 32) (dual of [19683, 19493, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(310, 39, F3, 5) (dual of [39, 29, 6]-code), using
- construction X applied to Ce(31) ⊂ Ce(25) [i] based on
- OOA 2-folding [i] based on linear OA(3200, 19722, F3, 32) (dual of [19722, 19522, 33]-code), using
(168, 200, 3129840)-Net in Base 3 — Upper bound on s
There is no (168, 200, 3129841)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 265614 118020 568465 347875 474375 145353 792339 366357 961569 209760 894858 614987 624659 303209 819751 074625 > 3200 [i]