MinT - Best Known (107−86, 107, s)-Nets in Base 16

Best Known (107−86, 107, s)-Nets in Base 16

(107−86, 107, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 107, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 107, 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]

(107−86, 107, 129)-Net over F₁₆ — Digital

Digital (21, 107, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 107, 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]

(107−86, 107, 1092)-Net in Base 16 — Upper bound on s

There is no (21, 107, 1093)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 712 415343 494591 475520 190895 850074 671184 984387 541988 070060 093725 131487 427419 643582 087486 867353 206996 655423 066763 654982 973603 933536 > 16¹⁰⁷ [i]