Best Known (99, 99+28, s)-Nets in Base 3
(99, 99+28, 464)-Net over F3 — Constructive and digital
Digital (99, 127, 464)-net over F3, using
- t-expansion [i] based on digital (98, 127, 464)-net over F3, using
- 1 times m-reduction [i] based on digital (98, 128, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 32, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 32, 116)-net over F81, using
- 1 times m-reduction [i] based on digital (98, 128, 464)-net over F3, using
(99, 99+28, 1093)-Net over F3 — Digital
Digital (99, 127, 1093)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3127, 1093, F3, 2, 28) (dual of [(1093, 2), 2059, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3127, 2186, F3, 28) (dual of [2186, 2059, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using
- OOA 2-folding [i] based on linear OA(3127, 2186, F3, 28) (dual of [2186, 2059, 29]-code), using
(99, 99+28, 64343)-Net in Base 3 — Upper bound on s
There is no (99, 127, 64344)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3 930065 514988 074841 374474 286165 958315 380164 966258 788193 157521 > 3127 [i]