Best Known (113, 113+34, s)-Nets in Base 3
(113, 113+34, 464)-Net over F3 — Constructive and digital
Digital (113, 147, 464)-net over F3, using
- 1 times m-reduction [i] based on digital (113, 148, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 37, 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, 37, 116)-net over F81, using
(113, 113+34, 896)-Net over F3 — Digital
Digital (113, 147, 896)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3147, 896, F3, 34) (dual of [896, 749, 35]-code), using
- 150 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 0, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 9 times 0, 1, 11 times 0, 1, 15 times 0, 1, 18 times 0, 1, 20 times 0, 1, 23 times 0, 1, 25 times 0) [i] based on linear OA(3130, 729, F3, 34) (dual of [729, 599, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- 150 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 0, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 9 times 0, 1, 11 times 0, 1, 15 times 0, 1, 18 times 0, 1, 20 times 0, 1, 23 times 0, 1, 25 times 0) [i] based on linear OA(3130, 729, F3, 34) (dual of [729, 599, 35]-code), using
(113, 113+34, 47913)-Net in Base 3 — Upper bound on s
There is no (113, 147, 47914)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 13703 905524 759882 509865 768622 113732 812491 553418 491057 847785 249993 394357 > 3147 [i]