Best Known (100, 128, s)-Nets in Base 4
(100, 128, 1044)-Net over F4 — Constructive and digital
Digital (100, 128, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 32, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
(100, 128, 3049)-Net over F4 — Digital
Digital (100, 128, 3049)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4128, 3049, F4, 28) (dual of [3049, 2921, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4128, 4109, F4, 28) (dual of [4109, 3981, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(25) [i] based on
- 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(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(41, 13, F4, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(4128, 4109, F4, 28) (dual of [4109, 3981, 29]-code), using
(100, 128, 643987)-Net in Base 4 — Upper bound on s
There is no (100, 128, 643988)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 115793 315353 092985 088610 796631 263506 304626 136125 508992 339641 296049 676632 016268 > 4128 [i]