MinT - Best Known (116−96, 116, s)-Nets in Base 16

Best Known (116−96, 116, s)-Nets in Base 16

(116−96, 116, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 116, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 116, 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]

(116−96, 116, 129)-Net over F₁₆ — Digital

Digital (20, 116, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 116, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(116−96, 116, 988)-Net in Base 16 — Upper bound on s

There is no (20, 116, 989)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 47 827725 497305 438522 471183 368642 910550 421909 450297 885281 483969 025203 083275 342902 428776 902084 550031 107593 375021 641023 999105 933260 912142 876706 > 16¹¹⁶ [i]