MinT - Best Known (109−103, 109, s)-Nets in Base 16

Best Known (109−103, 109, s)-Nets in Base 16

(109−103, 109, 65)-Net over F₁₆ — Constructive and digital

Digital (6, 109, 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]

(109−103, 109, 106)-Net in Base 16 — Upper bound on s

There is no (6, 109, 107)-net in base 16, because

13 times m-reduction [i] would yield (6, 96, 107)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16⁹⁶, 107, S₁₆, 90), but
  - the linear programming bound shows that MÂ â‰¥ 632381 165715 575607 270607 577961 002582 507033 932404 234102 073968 038308 365606 364351 282586 241545 781633 648349 739341 287044 099254 255616 / 15885 182313 > 16⁹⁶ [i]