MinT - Best Known (106−90, 106, s)-Nets in Base 16

Best Known (106−90, 106, s)-Nets in Base 16

(106−90, 106, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 106, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 106, 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]

(106−90, 106, 98)-Net over F₁₆ — Digital

Digital (16, 106, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 106, 98)-net over F₁₆, using
- net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
    - a curve from the manYPoints database [i]

(106−90, 106, 781)-Net in Base 16 — Upper bound on s

There is no (16, 106, 782)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 44 771357 017848 644583 344119 389722 217533 049349 152568 535849 527636 167667 058882 901820 479223 268130 645223 431928 020261 047507 192868 657976 > 16¹⁰⁶ [i]