Best Known (27, 27+83, s)-Nets in Base 27
(27, 27+83, 114)-Net over F27 — Constructive and digital
Digital (27, 110, 114)-net over F27, using
- t-expansion [i] based on digital (23, 110, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(27, 27+83, 208)-Net over F27 — Digital
Digital (27, 110, 208)-net over F27, using
- t-expansion [i] based on digital (24, 110, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(27, 27+83, 3943)-Net in Base 27 — Upper bound on s
There is no (27, 110, 3944)-net in base 27, because
- 1 times m-reduction [i] would yield (27, 109, 3944)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 046944 477029 735296 328828 189981 531687 806541 048474 591332 821136 292842 893626 665311 435442 997545 341366 627850 351119 180763 142680 636340 757395 645228 122426 762668 054545 > 27109 [i]