Best Known (30, 73, s)-Nets in Base 128
(30, 73, 417)-Net over F128 — Constructive and digital
Digital (30, 73, 417)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 21, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (9, 52, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- digital (0, 21, 129)-net over F128, using
(30, 73, 432)-Net in Base 128 — Constructive
(30, 73, 432)-net in base 128, using
- 1281 times duplication [i] based on (29, 72, 432)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 24, 257)-net in base 128, using
- base change [i] based on digital (0, 21, 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
- base change [i] based on digital (0, 21, 257)-net over F256, using
- digital (5, 48, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- (3, 24, 257)-net in base 128, using
- (u, u+v)-construction [i] based on
(30, 73, 620)-Net over F128 — Digital
Digital (30, 73, 620)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12873, 620, F128, 43) (dual of [620, 547, 44]-code), using
- 40 step Varšamov–Edel lengthening with (ri) = (1, 39 times 0) [i] based on linear OA(12872, 579, F128, 43) (dual of [579, 507, 44]-code), using
- construction X applied to AG(F,532P) ⊂ AG(F,534P) [i] based on
- linear OA(12871, 576, F128, 43) (dual of [576, 505, 44]-code), using algebraic-geometric code AG(F,532P) [i] based on function field F/F128 with g(F) = 28 and N(F) ≥ 577, using
- linear OA(12869, 576, F128, 41) (dual of [576, 507, 42]-code), using algebraic-geometric code AG(F,534P) [i] based on function field F/F128 with g(F) = 28 and N(F) ≥ 577 (see above)
- linear OA(1281, 3, F128, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to AG(F,532P) ⊂ AG(F,534P) [i] based on
- 40 step Varšamov–Edel lengthening with (ri) = (1, 39 times 0) [i] based on linear OA(12872, 579, F128, 43) (dual of [579, 507, 44]-code), using
(30, 73, 1146581)-Net in Base 128 — Upper bound on s
There is no (30, 73, 1146582)-net in base 128, because
- 1 times m-reduction [i] would yield (30, 72, 1146582)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 52 374826 424327 930355 244725 198378 367802 228260 608341 969260 965729 342921 167176 873368 639793 754383 163881 560996 644381 343975 543754 696030 787364 532292 299882 477195 > 12872 [i]