Best Known (174−36, 174, s)-Nets in Base 4
(174−36, 174, 1056)-Net over F4 — Constructive and digital
Digital (138, 174, 1056)-net over F4, using
- 42 times duplication [i] based on digital (136, 172, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 43, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
- trace code for nets [i] based on digital (7, 43, 264)-net over F256, using
(174−36, 174, 4606)-Net over F4 — Digital
Digital (138, 174, 4606)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4174, 4606, F4, 36) (dual of [4606, 4432, 37]-code), using
- 499 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0, 1, 38 times 0, 1, 60 times 0, 1, 88 times 0, 1, 118 times 0, 1, 145 times 0) [i] based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
- 1 times truncation [i] based on linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 1 times truncation [i] based on linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using
- 499 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0, 1, 38 times 0, 1, 60 times 0, 1, 88 times 0, 1, 118 times 0, 1, 145 times 0) [i] based on linear OA(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code), using
(174−36, 174, 1663099)-Net in Base 4 — Upper bound on s
There is no (138, 174, 1663100)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 573 376995 439957 395434 581743 114658 796607 423336 484961 550254 779051 109316 942896 240771 314271 185727 565093 517531 > 4174 [i]