Best Known (145−36, 145, s)-Nets in Base 5
(145−36, 145, 420)-Net over F5 — Constructive and digital
Digital (109, 145, 420)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (5, 23, 20)-net over F5, using
- net from sequence [i] based on digital (5, 19)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 5 and N(F) ≥ 20, using
- net from sequence [i] based on digital (5, 19)-sequence over F5, using
- digital (86, 122, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 61, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- trace code for nets [i] based on digital (25, 61, 200)-net over F25, using
- digital (5, 23, 20)-net over F5, using
(145−36, 145, 3065)-Net over F5 — Digital
Digital (109, 145, 3065)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5145, 3065, F5, 36) (dual of [3065, 2920, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(5145, 3144, F5, 36) (dual of [3144, 2999, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(31) [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(5126, 3125, F5, 32) (dual of [3125, 2999, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(54, 19, F5, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,5)), using
- construction X applied to Ce(35) ⊂ Ce(31) [i] based on
- discarding factors / shortening the dual code based on linear OA(5145, 3144, F5, 36) (dual of [3144, 2999, 37]-code), using
(145−36, 145, 806593)-Net in Base 5 — Upper bound on s
There is no (109, 145, 806594)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 224209 795410 160647 932097 471235 324645 290124 380423 025225 114990 125337 417634 853220 423799 777576 041303 414081 > 5145 [i]