Best Known (33, 33+43, s)-Nets in Base 81
(33, 33+43, 370)-Net over F81 — Constructive and digital
Digital (33, 76, 370)-net over F81, using
- t-expansion [i] based on digital (16, 76, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(33, 33+43, 608)-Net over F81 — Digital
Digital (33, 76, 608)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8176, 608, F81, 43) (dual of [608, 532, 44]-code), using
- 221 step Varšamov–Edel lengthening with (ri) = (9, 0, 1, 0, 0, 1, 6 times 0, 1, 11 times 0, 1, 18 times 0, 1, 29 times 0, 1, 40 times 0, 1, 49 times 0, 1, 56 times 0) [i] based on linear OA(8159, 370, F81, 43) (dual of [370, 311, 44]-code), using
- extended algebraic-geometric code AGe(F,326P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- 221 step Varšamov–Edel lengthening with (ri) = (9, 0, 1, 0, 0, 1, 6 times 0, 1, 11 times 0, 1, 18 times 0, 1, 29 times 0, 1, 40 times 0, 1, 49 times 0, 1, 56 times 0) [i] based on linear OA(8159, 370, F81, 43) (dual of [370, 311, 44]-code), using
(33, 33+43, 710254)-Net in Base 81 — Upper bound on s
There is no (33, 76, 710255)-net in base 81, because
- 1 times m-reduction [i] would yield (33, 75, 710255)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 136891 942399 235687 889059 452374 860233 838287 446829 110493 248867 616122 450438 318179 747606 317635 200366 016463 619065 038784 392614 490851 475292 251410 188401 > 8175 [i]