Best Known (114−30, 114, s)-Nets in Base 4
(114−30, 114, 531)-Net over F4 — Constructive and digital
Digital (84, 114, 531)-net over F4, using
- t-expansion [i] based on digital (83, 114, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 38, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 38, 177)-net over F64, using
(114−30, 114, 992)-Net over F4 — Digital
Digital (84, 114, 992)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4114, 992, F4, 30) (dual of [992, 878, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4114, 1037, F4, 30) (dual of [1037, 923, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- linear OA(4111, 1024, F4, 30) (dual of [1024, 913, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4101, 1024, F4, 27) (dual of [1024, 923, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(43, 13, F4, 2) (dual of [13, 10, 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(4114, 1037, F4, 30) (dual of [1037, 923, 31]-code), using
(114−30, 114, 80581)-Net in Base 4 — Upper bound on s
There is no (84, 114, 80582)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 431 379813 477175 770085 860026 971048 881039 051615 232129 112139 409417 427488 > 4114 [i]