Best Known (38, 60, s)-Nets in Base 7
(38, 60, 118)-Net over F7 — Constructive and digital
Digital (38, 60, 118)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (5, 16, 18)-net over F7, using
- 2 times m-reduction [i] based on digital (5, 18, 18)-net over F7, using
- digital (22, 44, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 22, 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, 22, 50)-net over F49, using
- digital (5, 16, 18)-net over F7, using
(38, 60, 391)-Net over F7 — Digital
Digital (38, 60, 391)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(760, 391, F7, 22) (dual of [391, 331, 23]-code), using
- 43 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 11 times 0, 1, 22 times 0) [i] based on 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]
- 43 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 11 times 0, 1, 22 times 0) [i] based on linear OA(755, 343, F7, 22) (dual of [343, 288, 23]-code), using
(38, 60, 33296)-Net in Base 7 — Upper bound on s
There is no (38, 60, 33297)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 508 094434 671831 383160 446902 076488 976269 782291 850903 > 760 [i]