Best Known (134−30, 134, s)-Nets in Base 4
(134−30, 134, 1040)-Net over F4 — Constructive and digital
Digital (104, 134, 1040)-net over F4, using
- 42 times duplication [i] based on digital (102, 132, 1040)-net over F4, using
- trace code for nets [i] based on digital (3, 33, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- trace code for nets [i] based on digital (3, 33, 260)-net over F256, using
(134−30, 134, 2705)-Net over F4 — Digital
Digital (104, 134, 2705)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4134, 2705, F4, 30) (dual of [2705, 2571, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4134, 4103, F4, 30) (dual of [4103, 3969, 31]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4133, 4102, F4, 30) (dual of [4102, 3969, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [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(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 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(29) ⊂ Ce(28) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4133, 4102, F4, 30) (dual of [4102, 3969, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4134, 4103, F4, 30) (dual of [4103, 3969, 31]-code), using
(134−30, 134, 511726)-Net in Base 4 — Upper bound on s
There is no (104, 134, 511727)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 474 293256 869678 645403 305393 421698 081211 090490 058343 226650 152540 842547 156941 950124 > 4134 [i]