Best Known (28−10, 28, s)-Nets in Base 5
(28−10, 28, 132)-Net over F5 — Constructive and digital
Digital (18, 28, 132)-net over F5, using
- trace code for nets [i] based on digital (4, 14, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
(28−10, 28, 162)-Net over F5 — Digital
Digital (18, 28, 162)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(528, 162, F5, 10) (dual of [162, 134, 11]-code), using
- 33 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 9 times 0, 1, 18 times 0) [i] based on linear OA(524, 125, F5, 10) (dual of [125, 101, 11]-code), using
- 1 times truncation [i] based on linear OA(525, 126, F5, 11) (dual of [126, 101, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 126 | 56−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(525, 126, F5, 11) (dual of [126, 101, 12]-code), using
- 33 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 9 times 0, 1, 18 times 0) [i] based on linear OA(524, 125, F5, 10) (dual of [125, 101, 11]-code), using
(28−10, 28, 5342)-Net in Base 5 — Upper bound on s
There is no (18, 28, 5343)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 37 270456 623432 428397 > 528 [i]