Best Known (66, 92, s)-Nets in Base 7
(66, 92, 228)-Net over F7 — Constructive and digital
Digital (66, 92, 228)-net over F7, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 14, 28)-net over F7, using
- 1 times m-reduction [i] based on digital (6, 15, 28)-net over F7, using
- digital (13, 26, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 13, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- trace code for nets [i] based on digital (0, 13, 50)-net over F49, using
- digital (26, 52, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 26, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- trace code for nets [i] based on digital (0, 26, 50)-net over F49, using
- digital (6, 14, 28)-net over F7, using
(66, 92, 2435)-Net over F7 — Digital
Digital (66, 92, 2435)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(792, 2435, F7, 26) (dual of [2435, 2343, 27]-code), using
- 27 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 21 times 0) [i] based on linear OA(789, 2405, F7, 26) (dual of [2405, 2316, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(789, 2401, F7, 26) (dual of [2401, 2312, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(785, 2401, F7, 25) (dual of [2401, 2316, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(70, 4, F7, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- 27 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 21 times 0) [i] based on linear OA(789, 2405, F7, 26) (dual of [2405, 2316, 27]-code), using
(66, 92, 903534)-Net in Base 7 — Upper bound on s
There is no (66, 92, 903535)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 561076 027316 069819 270699 299037 199361 224010 626813 430395 378273 288570 877347 178963 > 792 [i]