Best Known (106, 142, s)-Nets in Base 5
(106, 142, 416)-Net over F5 — Constructive and digital
Digital (106, 142, 416)-net over F5, using
- trace code for nets [i] based on digital (35, 71, 208)-net over F25, using
- net from sequence [i] based on digital (35, 207)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 35 and N(F) ≥ 208, using
- net from sequence [i] based on digital (35, 207)-sequence over F25, using
(106, 142, 2656)-Net over F5 — Digital
Digital (106, 142, 2656)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5142, 2656, F5, 36) (dual of [2656, 2514, 37]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(5142, 3131, F5, 36) (dual of [3131, 2989, 37]-code), using
(106, 142, 616818)-Net in Base 5 — Upper bound on s
There is no (106, 142, 616819)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1793 671672 897373 122065 679290 792201 379689 481418 639467 621018 689821 282019 843313 547251 299481 681382 931001 > 5142 [i]