Best Known (32−11, 32, s)-Nets in Base 5
(32−11, 32, 132)-Net over F5 — Constructive and digital
Digital (21, 32, 132)-net over F5, using
- 2 times m-reduction [i] based on digital (21, 34, 132)-net over F5, using
- trace code for nets [i] based on digital (4, 17, 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
- trace code for nets [i] based on digital (4, 17, 66)-net over F25, using
(32−11, 32, 201)-Net over F5 — Digital
Digital (21, 32, 201)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(532, 201, F5, 11) (dual of [201, 169, 12]-code), using
- 68 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 6 times 0, 1, 11 times 0, 1, 18 times 0, 1, 25 times 0) [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]
- 68 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 6 times 0, 1, 11 times 0, 1, 18 times 0, 1, 25 times 0) [i] based on linear OA(525, 126, F5, 11) (dual of [126, 101, 12]-code), using
(32−11, 32, 14037)-Net in Base 5 — Upper bound on s
There is no (21, 32, 14038)-net in base 5, because
- 1 times m-reduction [i] would yield (21, 31, 14038)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 4657 442743 953119 963353 > 531 [i]