Best Known (113, 113+36, s)-Nets in Base 4
(113, 113+36, 1032)-Net over F4 — Constructive and digital
Digital (113, 149, 1032)-net over F4, using
- 41 times duplication [i] based on digital (112, 148, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 37, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 37, 258)-net over F256, using
(113, 113+36, 1713)-Net over F4 — Digital
Digital (113, 149, 1713)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4149, 1713, F4, 36) (dual of [1713, 1564, 37]-code), using
- 1563 step Varšamov–Edel lengthening with (ri) = (10, 5, 3, 2, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 24 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 48 times 0, 1, 50 times 0, 1, 52 times 0, 1, 54 times 0, 1, 57 times 0, 1, 58 times 0, 1, 62 times 0, 1, 64 times 0) [i] based on linear OA(436, 37, F4, 36) (dual of [37, 1, 37]-code or 37-arc in PG(35,4)), using
- dual of repetition code with length 37 [i]
- 1563 step Varšamov–Edel lengthening with (ri) = (10, 5, 3, 2, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 24 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 48 times 0, 1, 50 times 0, 1, 52 times 0, 1, 54 times 0, 1, 57 times 0, 1, 58 times 0, 1, 62 times 0, 1, 64 times 0) [i] based on linear OA(436, 37, F4, 36) (dual of [37, 1, 37]-code or 37-arc in PG(35,4)), using
(113, 113+36, 242494)-Net in Base 4 — Upper bound on s
There is no (113, 149, 242495)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 509282 983548 047400 408339 265772 743764 455632 289307 507769 562184 986440 421324 395067 275381 645207 > 4149 [i]