Best Known (117−24, 117, s)-Nets in Base 4
(117−24, 117, 1051)-Net over F4 — Constructive and digital
Digital (93, 117, 1051)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (9, 21, 23)-net over F4, using
- 2 times m-reduction [i] based on digital (9, 23, 23)-net over F4, using
- digital (72, 96, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 24, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 24, 257)-net over F256, using
- digital (9, 21, 23)-net over F4, using
(117−24, 117, 4216)-Net over F4 — Digital
Digital (93, 117, 4216)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4117, 4216, F4, 24) (dual of [4216, 4099, 25]-code), using
- 111 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 9 times 0, 1, 17 times 0, 1, 28 times 0, 1, 44 times 0) [i] based on linear OA(4108, 4096, F4, 24) (dual of [4096, 3988, 25]-code), using
- 1 times truncation [i] based on linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using
- 111 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 9 times 0, 1, 17 times 0, 1, 28 times 0, 1, 44 times 0) [i] based on linear OA(4108, 4096, F4, 24) (dual of [4096, 3988, 25]-code), using
(117−24, 117, 1307139)-Net in Base 4 — Upper bound on s
There is no (93, 117, 1307140)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 27607 127808 893450 993405 930208 283752 215817 369773 404715 772600 033812 146048 > 4117 [i]