Best Known (29, 29+∞, s)-Nets in Base 9
(29, 29+∞, 78)-Net over F9 — Constructive and digital
Digital (29, m, 78)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (29, 77)-sequence over F9, using
- t-expansion [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- t-expansion [i] based on digital (22, 77)-sequence over F9, using
(29, 29+∞, 110)-Net over F9 — Digital
Digital (29, m, 110)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (29, 109)-sequence over F9, using
- t-expansion [i] based on digital (26, 109)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 26 and N(F) ≥ 110, using
- t-expansion [i] based on digital (26, 109)-sequence over F9, using
(29, 29+∞, 256)-Net in Base 9 — Upper bound on s
There is no (29, m, 257)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (29, 511, 257)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9511, 257, S9, 2, 482), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7343 373025 240060 856148 208498 969042 901766 392276 746768 819095 859657 200887 798806 216607 523209 215796 478218 669219 046286 819011 442804 965406 979163 552099 909627 328580 683845 771055 687164 091796 538059 055142 617616 245754 807251 398679 682257 535180 804242 698806 868465 969721 843330 272219 909290 810052 955818 948236 264877 606296 616745 313405 440213 040368 115509 032160 112206 278572 083270 462592 124441 310919 541201 673980 179626 722828 925047 877949 702866 216521 792800 111135 837940 018711 644511 571044 742069 059193 443950 860479 229637 010793 / 161 > 9511 [i]
- extracting embedded OOA [i] would yield OOA(9511, 257, S9, 2, 482), but