Best Known (98−25, 98, s)-Nets in Base 4
(98−25, 98, 531)-Net over F4 — Constructive and digital
Digital (73, 98, 531)-net over F4, using
- 1 times m-reduction [i] based on digital (73, 99, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 33, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 33, 177)-net over F64, using
(98−25, 98, 1062)-Net over F4 — Digital
Digital (73, 98, 1062)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(498, 1062, F4, 25) (dual of [1062, 964, 26]-code), using
- 30 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0) [i] based on linear OA(491, 1025, F4, 25) (dual of [1025, 934, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 410−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 30 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0) [i] based on linear OA(491, 1025, F4, 25) (dual of [1025, 934, 26]-code), using
(98−25, 98, 129676)-Net in Base 4 — Upper bound on s
There is no (73, 98, 129677)-net in base 4, because
- 1 times m-reduction [i] would yield (73, 97, 129677)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 25110 497478 080519 906037 478883 325549 054036 628579 773599 318785 > 497 [i]