Best Known (206, 246, s)-Nets in Base 3
(206, 246, 1488)-Net over F3 — Constructive and digital
Digital (206, 246, 1488)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 22, 8)-net over F3, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- digital (184, 224, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 56, 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, 56, 370)-net over F81, using
- digital (2, 22, 8)-net over F3, using
(206, 246, 9865)-Net over F3 — Digital
Digital (206, 246, 9865)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3246, 9865, F3, 2, 40) (dual of [(9865, 2), 19484, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3246, 19730, F3, 40) (dual of [19730, 19484, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(33) [i] based on
- linear OA(3235, 19683, F3, 40) (dual of [19683, 19448, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3199, 19683, F3, 34) (dual of [19683, 19484, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(311, 47, F3, 5) (dual of [47, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(39) ⊂ Ce(33) [i] based on
- OOA 2-folding [i] based on linear OA(3246, 19730, F3, 40) (dual of [19730, 19484, 41]-code), using
(206, 246, 3068067)-Net in Base 3 — Upper bound on s
There is no (206, 246, 3068068)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2354 128264 455914 038312 337659 969664 707211 097780 036707 878923 614810 903612 478861 473137 001304 673082 200840 944913 351781 029953 > 3246 [i]