Best Known (141−30, 141, s)-Nets in Base 4
(141−30, 141, 1048)-Net over F4 — Constructive and digital
Digital (111, 141, 1048)-net over F4, using
- 41 times duplication [i] based on digital (110, 140, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 35, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 35, 262)-net over F256, using
(141−30, 141, 3834)-Net over F4 — Digital
Digital (111, 141, 3834)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4141, 3834, F4, 30) (dual of [3834, 3693, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4141, 4128, F4, 30) (dual of [4128, 3987, 31]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4140, 4127, F4, 30) (dual of [4127, 3987, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(4133, 4096, F4, 30) (dual of [4096, 3963, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(47, 31, F4, 4) (dual of [31, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4140, 4127, F4, 30) (dual of [4127, 3987, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4141, 4128, F4, 30) (dual of [4128, 3987, 31]-code), using
(141−30, 141, 977246)-Net in Base 4 — Upper bound on s
There is no (111, 141, 977247)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7 770776 000374 288770 200646 060166 734210 089452 682333 570861 921271 909507 400469 901730 067716 > 4141 [i]