Best Known (202, 242, s)-Nets in Base 3
(202, 242, 1480)-Net over F3 — Constructive and digital
Digital (202, 242, 1480)-net over F3, using
- 6 times m-reduction [i] based on digital (202, 248, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 62, 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, 62, 370)-net over F81, using
(202, 242, 9078)-Net over F3 — Digital
Digital (202, 242, 9078)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3242, 9078, F3, 2, 40) (dual of [(9078, 2), 17914, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3242, 9855, F3, 2, 40) (dual of [(9855, 2), 19468, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3242, 19710, F3, 40) (dual of [19710, 19468, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(34) [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(3208, 19683, F3, 35) (dual of [19683, 19475, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(37, 27, F3, 4) (dual of [27, 20, 5]-code), using
- an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- construction X applied to Ce(39) ⊂ Ce(34) [i] based on
- OOA 2-folding [i] based on linear OA(3242, 19710, F3, 40) (dual of [19710, 19468, 41]-code), using
- discarding factors / shortening the dual code based on linear OOA(3242, 9855, F3, 2, 40) (dual of [(9855, 2), 19468, 41]-NRT-code), using
(202, 242, 2462861)-Net in Base 3 — Upper bound on s
There is no (202, 242, 2462862)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 29 063346 980422 486933 615785 918132 518854 645523 326389 289030 011438 015462 052817 346298 147705 950886 435603 410179 845206 053289 > 3242 [i]