Best Known (60, 78, s)-Nets in Base 4
(60, 78, 1032)-Net over F4 — Constructive and digital
Digital (60, 78, 1032)-net over F4, using
- 42 times duplication [i] based on digital (58, 76, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 19, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 19, 258)-net over F256, using
(60, 78, 1401)-Net over F4 — Digital
Digital (60, 78, 1401)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(478, 1401, F4, 18) (dual of [1401, 1323, 19]-code), using
- 360 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 10 times 0, 1, 18 times 0, 1, 30 times 0, 1, 45 times 0, 1, 63 times 0, 1, 80 times 0, 1, 97 times 0) [i] based on linear OA(466, 1029, F4, 18) (dual of [1029, 963, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(466, 1024, F4, 18) (dual of [1024, 958, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(461, 1024, F4, 17) (dual of [1024, 963, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- 360 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 10 times 0, 1, 18 times 0, 1, 30 times 0, 1, 45 times 0, 1, 63 times 0, 1, 80 times 0, 1, 97 times 0) [i] based on linear OA(466, 1029, F4, 18) (dual of [1029, 963, 19]-code), using
(60, 78, 228281)-Net in Base 4 — Upper bound on s
There is no (60, 78, 228282)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 91346 756155 436010 392715 781471 735914 877980 047773 > 478 [i]