Best Known (84, 108, s)-Nets in Base 4
(84, 108, 1040)-Net over F4 — Constructive and digital
Digital (84, 108, 1040)-net over F4, using
- trace code for nets [i] based on digital (3, 27, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
(84, 108, 2541)-Net over F4 — Digital
Digital (84, 108, 2541)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4108, 2541, F4, 24) (dual of [2541, 2433, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4108, 4096, F4, 24) (dual of [4096, 3988, 25]-code), using
- 1 times truncation [i] based on linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4108, 4096, F4, 24) (dual of [4096, 3988, 25]-code), using
(84, 108, 462137)-Net in Base 4 — Upper bound on s
There is no (84, 108, 462138)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 105313 825403 177852 544755 932384 337252 354397 620401 866902 882474 760724 > 4108 [i]