Best Known (152, 152+38, s)-Nets in Base 3
(152, 152+38, 688)-Net over F3 — Constructive and digital
Digital (152, 190, 688)-net over F3, using
- t-expansion [i] based on digital (151, 190, 688)-net over F3, using
- 2 times m-reduction [i] based on digital (151, 192, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 48, 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, 48, 172)-net over F81, using
- 2 times m-reduction [i] based on digital (151, 192, 688)-net over F3, using
(152, 152+38, 2250)-Net over F3 — Digital
Digital (152, 190, 2250)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3190, 2250, F3, 38) (dual of [2250, 2060, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(3190, 2272, F3, 38) (dual of [2272, 2082, 39]-code), using
- 64 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 9 times 0, 1, 12 times 0, 1, 16 times 0) [i] based on linear OA(3176, 2194, F3, 38) (dual of [2194, 2018, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(36) [i] based on
- linear OA(3176, 2187, F3, 38) (dual of [2187, 2011, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(30, 7, F3, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(37) ⊂ Ce(36) [i] based on
- 64 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 9 times 0, 1, 12 times 0, 1, 16 times 0) [i] based on linear OA(3176, 2194, F3, 38) (dual of [2194, 2018, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(3190, 2272, F3, 38) (dual of [2272, 2082, 39]-code), using
(152, 152+38, 234079)-Net in Base 3 — Upper bound on s
There is no (152, 190, 234080)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 4 498308 769696 385109 080100 397483 607102 874390 294106 313116 711677 183145 384416 181844 489038 595457 > 3190 [i]