Best Known (70, 102, s)-Nets in Base 5
(70, 102, 296)-Net over F5 — Constructive and digital
Digital (70, 102, 296)-net over F5, using
- trace code for nets [i] based on digital (19, 51, 148)-net over F25, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
(70, 102, 648)-Net over F5 — Digital
Digital (70, 102, 648)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5102, 648, F5, 32) (dual of [648, 546, 33]-code), using
- 16 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 11 times 0) [i] based on linear OA(599, 629, F5, 32) (dual of [629, 530, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(599, 625, F5, 32) (dual of [625, 526, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(595, 625, F5, 31) (dual of [625, 530, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- 16 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 11 times 0) [i] based on linear OA(599, 629, F5, 32) (dual of [629, 530, 33]-code), using
(70, 102, 48563)-Net in Base 5 — Upper bound on s
There is no (70, 102, 48564)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 197249 812629 324555 292747 713711 166541 452216 771307 209154 167080 097333 673985 > 5102 [i]