Best Known (159, 159+46, s)-Nets in Base 4
(159, 159+46, 1048)-Net over F4 — Constructive and digital
Digital (159, 205, 1048)-net over F4, using
- 41 times duplication [i] based on digital (158, 204, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 51, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 51, 262)-net over F256, using
(159, 159+46, 3523)-Net over F4 — Digital
Digital (159, 205, 3523)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4205, 3523, F4, 46) (dual of [3523, 3318, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(4205, 4096, F4, 46) (dual of [4096, 3891, 47]-code), using
- an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- discarding factors / shortening the dual code based on linear OA(4205, 4096, F4, 46) (dual of [4096, 3891, 47]-code), using
(159, 159+46, 730315)-Net in Base 4 — Upper bound on s
There is no (159, 205, 730316)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2644 225498 890232 807747 583428 301385 230942 979422 079667 514654 595133 405193 636197 907816 323269 164591 959778 594160 676481 250777 683896 > 4205 [i]