Best Known (104, 104+29, s)-Nets in Base 4
(104, 104+29, 1044)-Net over F4 — Constructive and digital
Digital (104, 133, 1044)-net over F4, using
- 41 times duplication [i] based on digital (103, 132, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 33, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- trace code for nets [i] based on digital (4, 33, 261)-net over F256, using
(104, 104+29, 3176)-Net over F4 — Digital
Digital (104, 133, 3176)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4133, 3176, F4, 29) (dual of [3176, 3043, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4133, 4097, F4, 29) (dual of [4097, 3964, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4133, 4097, F4, 29) (dual of [4097, 3964, 30]-code), using
(104, 104+29, 956967)-Net in Base 4 — Upper bound on s
There is no (104, 133, 956968)-net in base 4, because
- 1 times m-reduction [i] would yield (104, 132, 956968)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 29 643124 660141 621892 913011 547093 031956 344195 635553 504995 536080 485120 465632 946060 > 4132 [i]