Best Known (99, 126, s)-Nets in Base 3
(99, 126, 600)-Net over F3 — Constructive and digital
Digital (99, 126, 600)-net over F3, using
- 32 times duplication [i] based on digital (97, 124, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 31, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 31, 150)-net over F81, using
(99, 126, 1214)-Net over F3 — Digital
Digital (99, 126, 1214)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3126, 1214, F3, 27) (dual of [1214, 1088, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3126, 2186, F3, 27) (dual of [2186, 2060, 28]-code), using
- 1 times truncation [i] 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]
- 1 times truncation [i] based on linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3126, 2186, F3, 27) (dual of [2186, 2060, 28]-code), using
(99, 126, 109655)-Net in Base 3 — Upper bound on s
There is no (99, 126, 109656)-net in base 3, because
- 1 times m-reduction [i] would yield (99, 125, 109656)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 436691 099993 430215 788181 682305 451455 170768 471982 916216 403377 > 3125 [i]