Best Known (103, 103+30, s)-Nets in Base 4
(103, 103+30, 1040)-Net over F4 — Constructive and digital
Digital (103, 133, 1040)-net over F4, using
- 41 times duplication [i] based on digital (102, 132, 1040)-net over F4, using
- trace code for nets [i] based on digital (3, 33, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- trace code for nets [i] based on digital (3, 33, 260)-net over F256, using
(103, 103+30, 2573)-Net over F4 — Digital
Digital (103, 133, 2573)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4133, 2573, F4, 30) (dual of [2573, 2440, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4133, 4096, F4, 30) (dual of [4096, 3963, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(4133, 4096, F4, 30) (dual of [4096, 3963, 31]-code), using
(103, 103+30, 466551)-Net in Base 4 — Upper bound on s
There is no (103, 133, 466552)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 118 573487 316378 265752 739760 388800 424688 703631 251522 678946 711840 800051 683611 034234 > 4133 [i]