Best Known (202−32, 202, s)-Nets in Base 3
(202−32, 202, 1480)-Net over F3 — Constructive and digital
Digital (170, 202, 1480)-net over F3, using
- t-expansion [i] based on digital (169, 202, 1480)-net over F3, using
- 2 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
- 2 times m-reduction [i] based on digital (169, 204, 1480)-net over F3, using
(202−32, 202, 9865)-Net over F3 — Digital
Digital (170, 202, 9865)-net over F3, using
- 31 times duplication [i] based on digital (169, 201, 9865)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [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
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3201, 9865, F3, 2, 32) (dual of [(9865, 2), 19529, 33]-NRT-code), using
(202−32, 202, 3590564)-Net in Base 3 — Upper bound on s
There is no (170, 202, 3590565)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 390534 545727 667158 681731 029456 054711 171182 023044 005558 557770 739561 928418 584805 938610 847900 952001 > 3202 [i]