Best Known (98, 124, s)-Nets in Base 4
(98, 124, 1049)-Net over F4 — Constructive and digital
Digital (98, 124, 1049)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (7, 20, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (78, 104, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 26, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 26, 257)-net over F256, using
- digital (7, 20, 21)-net over F4, using
(98, 124, 3960)-Net over F4 — Digital
Digital (98, 124, 3960)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4124, 3960, F4, 26) (dual of [3960, 3836, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4124, 4130, F4, 26) (dual of [4130, 4006, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- linear OA(4115, 4096, F4, 26) (dual of [4096, 3981, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(485, 4096, F4, 19) (dual of [4096, 4011, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(47, 32, F4, 4) (dual of [32, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(25) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(4124, 4130, F4, 26) (dual of [4130, 4006, 27]-code), using
(98, 124, 1044736)-Net in Base 4 — Upper bound on s
There is no (98, 124, 1044737)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 452 316594 837946 657279 540883 150931 467092 827774 136895 640299 284582 656784 728064 > 4124 [i]