Best Known (135, 135+38, s)-Nets in Base 4
(135, 135+38, 1048)-Net over F4 — Constructive and digital
Digital (135, 173, 1048)-net over F4, using
- 41 times duplication [i] based on digital (134, 172, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 43, 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, 43, 262)-net over F256, using
(135, 135+38, 3554)-Net over F4 — Digital
Digital (135, 173, 3554)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4173, 3554, F4, 38) (dual of [3554, 3381, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(4173, 4113, F4, 38) (dual of [4113, 3940, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4151, 4096, F4, 34) (dual of [4096, 3945, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- discarding factors / shortening the dual code based on linear OA(4173, 4113, F4, 38) (dual of [4113, 3940, 39]-code), using
(135, 135+38, 801679)-Net in Base 4 — Upper bound on s
There is no (135, 173, 801680)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 143 346460 307661 858180 891782 599573 535899 431929 975673 975360 534423 964112 269502 785803 942765 130629 718662 628984 > 4173 [i]