Best Known (38, 38+24, s)-Nets in Base 7
(38, 38+24, 114)-Net over F7 — Constructive and digital
Digital (38, 62, 114)-net over F7, using
- trace code for nets [i] based on digital (7, 31, 57)-net over F49, using
- net from sequence [i] based on digital (7, 56)-sequence over F49, using
(38, 38+24, 321)-Net over F7 — Digital
Digital (38, 62, 321)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(762, 321, F7, 24) (dual of [321, 259, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(762, 350, F7, 24) (dual of [350, 288, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(761, 343, F7, 24) (dual of [343, 282, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(755, 343, F7, 22) (dual of [343, 288, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(762, 350, F7, 24) (dual of [350, 288, 25]-code), using
(38, 38+24, 20482)-Net in Base 7 — Upper bound on s
There is no (38, 62, 20483)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 24894 790690 492420 766673 208404 424132 885158 872151 321049 > 762 [i]