Best Known (84, 109, s)-Nets in Base 4
(84, 109, 1036)-Net over F4 — Constructive and digital
Digital (84, 109, 1036)-net over F4, using
- 41 times duplication [i] based on digital (83, 108, 1036)-net over F4, using
- trace code for nets [i] based on digital (2, 27, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 27, 259)-net over F256, using
(84, 109, 2093)-Net over F4 — Digital
Digital (84, 109, 2093)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4109, 2093, F4, 25) (dual of [2093, 1984, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using
(84, 109, 462137)-Net in Base 4 — Upper bound on s
There is no (84, 109, 462138)-net in base 4, because
- 1 times m-reduction [i] would yield (84, 108, 462138)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 105313 825403 177852 544755 932384 337252 354397 620401 866902 882474 760724 > 4108 [i]