Best Known (98, 135, s)-Nets in Base 8
(98, 135, 1026)-Net over F8 — Constructive and digital
Digital (98, 135, 1026)-net over F8, using
- 5 times m-reduction [i] based on digital (98, 140, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 70, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 70, 513)-net over F64, using
(98, 135, 4987)-Net over F8 — Digital
Digital (98, 135, 4987)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8135, 4987, F8, 37) (dual of [4987, 4852, 38]-code), using
- 4851 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 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, 4 times 0, 1, 4 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, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 50 times 0, 1, 54 times 0, 1, 57 times 0, 1, 60 times 0, 1, 63 times 0, 1, 68 times 0, 1, 72 times 0, 1, 76 times 0, 1, 81 times 0, 1, 86 times 0, 1, 91 times 0, 1, 97 times 0, 1, 102 times 0, 1, 109 times 0, 1, 115 times 0, 1, 122 times 0, 1, 130 times 0, 1, 137 times 0, 1, 146 times 0, 1, 154 times 0, 1, 164 times 0, 1, 174 times 0, 1, 184 times 0, 1, 195 times 0, 1, 207 times 0, 1, 219 times 0, 1, 233 times 0, 1, 246 times 0, 1, 262 times 0, 1, 277 times 0) [i] based on linear OA(837, 38, F8, 37) (dual of [38, 1, 38]-code or 38-arc in PG(36,8)), using
- dual of repetition code with length 38 [i]
- 4851 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 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, 4 times 0, 1, 4 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, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 50 times 0, 1, 54 times 0, 1, 57 times 0, 1, 60 times 0, 1, 63 times 0, 1, 68 times 0, 1, 72 times 0, 1, 76 times 0, 1, 81 times 0, 1, 86 times 0, 1, 91 times 0, 1, 97 times 0, 1, 102 times 0, 1, 109 times 0, 1, 115 times 0, 1, 122 times 0, 1, 130 times 0, 1, 137 times 0, 1, 146 times 0, 1, 154 times 0, 1, 164 times 0, 1, 174 times 0, 1, 184 times 0, 1, 195 times 0, 1, 207 times 0, 1, 219 times 0, 1, 233 times 0, 1, 246 times 0, 1, 262 times 0, 1, 277 times 0) [i] based on linear OA(837, 38, F8, 37) (dual of [38, 1, 38]-code or 38-arc in PG(36,8)), using
(98, 135, 5702094)-Net in Base 8 — Upper bound on s
There is no (98, 135, 5702095)-net in base 8, because
- 1 times m-reduction [i] would yield (98, 134, 5702095)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 10 329016 078330 578582 597533 791582 632947 817371 663467 784503 125706 525880 694985 399693 359423 044060 254065 481476 133712 581259 276500 > 8134 [i]