MinT - Best Known (78−71, 78, s)-Nets in Base 16

Best Known (78−71, 78, s)-Nets in Base 16

(78−71, 78, 65)-Net over F₁₆ — Constructive and digital

Digital (7, 78, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 78, 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]

(78−71, 78, 281)-Net in Base 16 — Upper bound on s

There is no (7, 78, 282)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁷⁸, 282, S₁₆, 71), but
- the linear programming bound shows that MÂ â‰¥ 6 606718 883264 289538 399533 883845 708613 399509 471683 845616 345400 558079 611592 560996 174039 917039 601574 093316 187592 847845 755834 308616 762993 633302 985700 573551 001600 / 770 170750 151456 739914 211650 781645 222579 844141 705823 657904 450739 > 16⁷⁸ [i]