Best Known (18, 18+11, s)-Nets in Base 5
(18, 18+11, 104)-Net over F5 — Constructive and digital
Digital (18, 29, 104)-net over F5, using
- 1 times m-reduction [i] based on digital (18, 30, 104)-net over F5, using
- trace code for nets [i] based on digital (3, 15, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- trace code for nets [i] based on digital (3, 15, 52)-net over F25, using
(18, 18+11, 141)-Net over F5 — Digital
Digital (18, 29, 141)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(529, 141, F5, 11) (dual of [141, 112, 12]-code), using
- 11 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 6 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]
- 11 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 6 times 0) [i] based on linear OA(525, 126, F5, 11) (dual of [126, 101, 12]-code), using
(18, 18+11, 5342)-Net in Base 5 — Upper bound on s
There is no (18, 29, 5343)-net in base 5, because
- 1 times m-reduction [i] would yield (18, 28, 5343)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 37 270456 623432 428397 > 528 [i]