Best Known (98, 98+28, s)-Nets in Base 5
(98, 98+28, 504)-Net over F5 — Constructive and digital
Digital (98, 126, 504)-net over F5, using
- t-expansion [i] based on digital (97, 126, 504)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (34, 48, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 24, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 24, 126)-net over F25, using
- digital (49, 78, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 39, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- trace code for nets [i] based on digital (10, 39, 126)-net over F25, using
- digital (34, 48, 252)-net over F5, using
- (u, u+v)-construction [i] based on
(98, 98+28, 5005)-Net over F5 — Digital
Digital (98, 126, 5005)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5126, 5005, F5, 28) (dual of [5005, 4879, 29]-code), using
- 4878 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 34 times 0, 1, 36 times 0, 1, 38 times 0, 1, 41 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 76 times 0, 1, 81 times 0, 1, 86 times 0, 1, 91 times 0, 1, 96 times 0, 1, 103 times 0, 1, 109 times 0, 1, 117 times 0, 1, 123 times 0, 1, 131 times 0, 1, 139 times 0, 1, 148 times 0, 1, 157 times 0, 1, 167 times 0, 1, 177 times 0, 1, 189 times 0, 1, 200 times 0, 1, 212 times 0, 1, 226 times 0, 1, 239 times 0, 1, 255 times 0, 1, 270 times 0, 1, 287 times 0) [i] based on linear OA(528, 29, F5, 28) (dual of [29, 1, 29]-code or 29-arc in PG(27,5)), using
- dual of repetition code with length 29 [i]
- 4878 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 34 times 0, 1, 36 times 0, 1, 38 times 0, 1, 41 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 76 times 0, 1, 81 times 0, 1, 86 times 0, 1, 91 times 0, 1, 96 times 0, 1, 103 times 0, 1, 109 times 0, 1, 117 times 0, 1, 123 times 0, 1, 131 times 0, 1, 139 times 0, 1, 148 times 0, 1, 157 times 0, 1, 167 times 0, 1, 177 times 0, 1, 189 times 0, 1, 200 times 0, 1, 212 times 0, 1, 226 times 0, 1, 239 times 0, 1, 255 times 0, 1, 270 times 0, 1, 287 times 0) [i] based on linear OA(528, 29, F5, 28) (dual of [29, 1, 29]-code or 29-arc in PG(27,5)), using
(98, 98+28, 2952067)-Net in Base 5 — Upper bound on s
There is no (98, 126, 2952068)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 11754 959093 308080 301624 411469 161616 899577 512316 037848 256859 347659 274907 734137 392366 119105 > 5126 [i]