Best Known (203−32, 203, s)-Nets in Base 3
(203−32, 203, 1480)-Net over F3 — Constructive and digital
Digital (171, 203, 1480)-net over F3, using
- t-expansion [i] based on digital (169, 203, 1480)-net over F3, using
- 1 times m-reduction [i] based on digital (169, 204, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 51, 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, 51, 370)-net over F81, using
- 1 times m-reduction [i] based on digital (169, 204, 1480)-net over F3, using
(203−32, 203, 9866)-Net over F3 — Digital
Digital (171, 203, 9866)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3203, 9866, F3, 2, 32) (dual of [(9866, 2), 19529, 33]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3201, 9865, F3, 2, 32) (dual of [(9865, 2), 19529, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3201, 19730, F3, 32) (dual of [19730, 19529, 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(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(31) ⊂ Ce(25) [i] based on
- OOA 2-folding [i] based on linear OA(3201, 19730, F3, 32) (dual of [19730, 19529, 33]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3201, 9865, F3, 2, 32) (dual of [(9865, 2), 19529, 33]-NRT-code), using
(203−32, 203, 3845766)-Net in Base 3 — Upper bound on s
There is no (171, 203, 3845767)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 7 171596 370570 258645 513015 084162 092070 465189 014108 658873 244632 050006 773159 771460 868632 350402 488545 > 3203 [i]