MinT - Best Known (125−116, 125, s)-Nets in Base 16

Best Known (125−116, 125, s)-Nets in Base 16

Digital (9, 125, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 125, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

Digital (9, 125, 72)-net over F₁₆, using

There is no (9, 125, 239)-net in base 16, because

6 times m-reduction [i] would yield (9, 119, 239)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16¹¹⁹, 239, S₁₆, 110), but
  - the linear programming bound shows that MÂ â‰¥ 105 751261 851445 651241 223376 310284 179577 966501 260705 356346 227564 202565 523994 885023 748885 368966 674955 643854 545983 753998 603948 428988 233078 709660 014456 840468 150268 019297 890282 967687 615194 509971 863793 395558 270619 539369 490508 421690 452437 884748 169216 / 514 230046 016904 481280 869495 709155 959659 255292 094061 582196 061661 819297 527117 705225 065781 635987 576681 > 16¹¹⁹ [i]