Best Known (111, 111+36, s)-Nets in Base 5
(111, 111+36, 460)-Net over F5 — Constructive and digital
Digital (111, 147, 460)-net over F5, using
- 1 times m-reduction [i] based on digital (111, 148, 460)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (36, 54, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 27, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- trace code for nets [i] based on digital (9, 27, 104)-net over F25, using
- digital (57, 94, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 47, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 47, 126)-net over F25, using
- digital (36, 54, 208)-net over F5, using
- (u, u+v)-construction [i] based on
(111, 111+36, 3189)-Net over F5 — Digital
Digital (111, 147, 3189)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5147, 3189, F5, 36) (dual of [3189, 3042, 37]-code), using
- 53 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 14 times 0, 1, 29 times 0) [i] based on linear OA(5142, 3131, F5, 36) (dual of [3131, 2989, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(33) [i] based on
- linear OA(5141, 3125, F5, 36) (dual of [3125, 2984, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(5136, 3125, F5, 34) (dual of [3125, 2989, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(51, 6, F5, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(35) ⊂ Ce(33) [i] based on
- 53 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 14 times 0, 1, 29 times 0) [i] based on linear OA(5142, 3131, F5, 36) (dual of [3131, 2989, 37]-code), using
(111, 111+36, 964537)-Net in Base 5 — Upper bound on s
There is no (111, 147, 964538)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 5 605215 887759 861284 822120 924687 774952 342841 699739 404218 529486 397141 724484 313910 748121 803467 647712 050625 > 5147 [i]