Best Known (165, 197, s)-Nets in Base 3
(165, 197, 1480)-Net over F3 — Constructive and digital
Digital (165, 197, 1480)-net over F3, using
- 31 times duplication [i] based on digital (164, 196, 1480)-net over F3, using
- t-expansion [i] based on digital (163, 196, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 49, 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, 49, 370)-net over F81, using
- t-expansion [i] based on digital (163, 196, 1480)-net over F3, using
(165, 197, 9398)-Net over F3 — Digital
Digital (165, 197, 9398)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3197, 9398, F3, 2, 32) (dual of [(9398, 2), 18599, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3197, 9858, F3, 2, 32) (dual of [(9858, 2), 19519, 33]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3196, 9858, F3, 2, 32) (dual of [(9858, 2), 19520, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3196, 19716, F3, 32) (dual of [19716, 19520, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(27) [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(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(36, 33, F3, 3) (dual of [33, 27, 4]-code or 33-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- OOA 2-folding [i] based on linear OA(3196, 19716, F3, 32) (dual of [19716, 19520, 33]-code), using
- 31 times duplication [i] based on linear OOA(3196, 9858, F3, 2, 32) (dual of [(9858, 2), 19520, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3197, 9858, F3, 2, 32) (dual of [(9858, 2), 19519, 33]-NRT-code), using
(165, 197, 2547191)-Net in Base 3 — Upper bound on s
There is no (165, 197, 2547192)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 9837 608459 420668 479533 850695 377911 346656 928346 416101 924119 371868 975175 367203 354639 619692 038145 > 3197 [i]