Best Known (77, 113, s)-Nets in Base 5
(77, 113, 296)-Net over F5 — Constructive and digital
Digital (77, 113, 296)-net over F5, using
- 3 times m-reduction [i] based on digital (77, 116, 296)-net over F5, using
- trace code for nets [i] based on digital (19, 58, 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
- trace code for nets [i] based on digital (19, 58, 148)-net over F25, using
(77, 113, 650)-Net over F5 — Digital
Digital (77, 113, 650)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5113, 650, F5, 36) (dual of [650, 537, 37]-code), using
- 23 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 16 times 0) [i] based on linear OA(5111, 625, F5, 36) (dual of [625, 514, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 23 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 16 times 0) [i] based on linear OA(5111, 625, F5, 36) (dual of [625, 514, 37]-code), using
(77, 113, 46123)-Net in Base 5 — Upper bound on s
There is no (77, 113, 46124)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 9 630014 220413 343739 886028 977928 884000 392837 844787 136618 971008 383769 477642 910529 > 5113 [i]