Best Known (88, 114, s)-Nets in Base 5
(88, 114, 416)-Net over F5 — Constructive and digital
Digital (88, 114, 416)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (31, 44, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 22, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- trace code for nets [i] based on digital (9, 22, 104)-net over F25, using
- digital (44, 70, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 35, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25 (see above)
- trace code for nets [i] based on digital (9, 35, 104)-net over F25, using
- digital (31, 44, 208)-net over F5, using
(88, 114, 3942)-Net over F5 — Digital
Digital (88, 114, 3942)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5114, 3942, F5, 26) (dual of [3942, 3828, 27]-code), using
- 804 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 23 times 0, 1, 39 times 0, 1, 64 times 0, 1, 99 times 0, 1, 141 times 0, 1, 184 times 0, 1, 222 times 0) [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 804 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 23 times 0, 1, 39 times 0, 1, 64 times 0, 1, 99 times 0, 1, 141 times 0, 1, 184 times 0, 1, 222 times 0) [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
(88, 114, 1908856)-Net in Base 5 — Upper bound on s
There is no (88, 114, 1908857)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 48 148311 681413 889768 826845 459586 432045 646448 163570 138719 055593 812388 360571 262325 > 5114 [i]