MinT - Best Known (98−49, 98, s)-Nets in Base 16

Best Known (98−49, 98, s)-Nets in Base 16

(98−49, 98, 514)-Net over F₁₆ — Constructive and digital

Digital (49, 98, 514)-net over F₁₆, using

trace code for nets [i] based on digital (0, 49, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(98−49, 98, 48062)-Net in Base 16 — Upper bound on s

There is no (49, 98, 48063)-net in base 16, because

1 times m-reduction [i] would yield (49, 97, 48063)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 630 646321 806500 576058 066431 012089 647437 907937 583919 039680 219828 280738 153540 276969 444962 510814 288353 908898 083465 188781 > 16⁹⁷ [i]