Best Known (181, 181+34, s)-Nets in Base 3
(181, 181+34, 1480)-Net over F3 — Constructive and digital
Digital (181, 215, 1480)-net over F3, using
- 5 times m-reduction [i] based on digital (181, 220, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 55, 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, 55, 370)-net over F81, using
(181, 181+34, 9891)-Net over F3 — Digital
Digital (181, 215, 9891)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3215, 9891, F3, 34) (dual of [9891, 9676, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3215, 19744, F3, 34) (dual of [19744, 19529, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- 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(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(316, 61, F3, 7) (dual of [61, 45, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3215, 19744, F3, 34) (dual of [19744, 19529, 35]-code), using
(181, 181+34, 3882343)-Net in Base 3 — Upper bound on s
There is no (181, 215, 3882344)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3 811281 495840 753928 851980 900098 795927 585841 662100 573525 313334 120025 533153 423545 190929 510866 768426 749905 > 3215 [i]