Best Known (106, 136, s)-Nets in Base 4
(106, 136, 1044)-Net over F4 — Constructive and digital
Digital (106, 136, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 34, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
(106, 136, 2989)-Net over F4 — Digital
Digital (106, 136, 2989)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4136, 2989, F4, 30) (dual of [2989, 2853, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4136, 4111, F4, 30) (dual of [4111, 3975, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [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(4121, 4096, F4, 27) (dual of [4096, 3975, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(43, 15, F4, 2) (dual of [15, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(4136, 4111, F4, 30) (dual of [4111, 3975, 31]-code), using
(106, 136, 615622)-Net in Base 4 — Upper bound on s
There is no (106, 136, 615623)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7588 723746 423574 389692 215702 231121 228667 649113 235377 372888 018090 977038 691820 405856 > 4136 [i]