Best Known (126−24, 126, s)-Nets in Base 3
(126−24, 126, 688)-Net over F3 — Constructive and digital
Digital (102, 126, 688)-net over F3, using
- 32 times duplication [i] based on digital (100, 124, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 31, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 31, 172)-net over F81, using
(126−24, 126, 2290)-Net over F3 — Digital
Digital (102, 126, 2290)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3126, 2290, F3, 24) (dual of [2290, 2164, 25]-code), using
- 89 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 9 times 0, 1, 13 times 0, 1, 17 times 0, 1, 24 times 0) [i] based on linear OA(3112, 2187, F3, 24) (dual of [2187, 2075, 25]-code), using
- 1 times truncation [i] based on linear OA(3113, 2188, F3, 25) (dual of [2188, 2075, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3113, 2188, F3, 25) (dual of [2188, 2075, 26]-code), using
- 89 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 9 times 0, 1, 13 times 0, 1, 17 times 0, 1, 24 times 0) [i] based on linear OA(3112, 2187, F3, 24) (dual of [2187, 2075, 25]-code), using
(126−24, 126, 270449)-Net in Base 3 — Upper bound on s
There is no (102, 126, 270450)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 310051 618327 692876 694416 738947 754329 223179 485989 085087 173241 > 3126 [i]